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Right Triangle Trigonometry Worksheets – Full Set (Free Download)

  • October 22, 2022
  • Math Worksheets

In this article we have covered wide variety of Right Triangle Trigonometry Worksheets that are suitable for middle schoolers. For each section, we have given the methodology that can be used to solve the problems in the worksheet.

Feel free to download and print (for personal use) and try these intuitive trigonometry problems.

Applications of Right Triangle Trigonometry Worksheet

To solve these problems, you will have to first learn the concept of the Pythagorean Theorem and the law of tangents.  

The Pythagorean Theorem  – Is about the relationship between the three sides of a right-angle triangle. So, if ABC is a right-angle triangle in which the three sides are AB, BC, and AC, AB 2 + BC 2 =AC 2 . Here, AC is the hypotenuse-the longest side of the right angle triangle. 

Applications of Right Triangle Trigonometry - Pythagorean Theorem

You are needed to use the above formula to determine the unknown side of the right-angled triangle when two sides are already given.

Law of tangents  – It is the relationship between any two sides and the two angles opposite to these two sides of a right-angled triangle ABC. Remember, the law of tangent applies to only right-angle triangles. 

Again tangent of a given angle of a right-angled triangle is the ratio of its opposite side to its adjacent side. 

So, here tanC=AB/BC

Example of finding the length of a side.

Calculate the length of x and y of two right-angle triangles in the figure below that share two vertices and one common straight-line base. Here the length of one side AB is 12, D=60 0 and angle C=30 0 .

Applications of Right Triangle Trigonometry - Law of Tangents

To solve the above problem, you have to do the following steps.

Step 1. For triangle ABD, you already have AB=12, B=90 0 and D=60 0

So, tan 60 0 =opposite side/adjacent side

                  =AB/BD

                  =12/BD

                  =12/x

Since it is known from the trigonometry table that tan 60 0 =√3,   you can write

So, x=12/√3

        =3×4/√3

        =√3x√3 x4/√3

        =4√3

Step 2 For triangle ABC, you already have AB=12, B=90 0 and C=30 0

So, tan 30 0 =opposite side/adjacent side

                  =AB/BC

                  =12/(BD +DC)

                  =12/(x+y)

Since it is known from the trigonometry table that tan 30 0 =1/√3,   you can write

1/√3=12/(4√3 +y)

So, (4√3 +y)=12x√3

                 y =12√3-4√3

                    =√3(12-4)

                    =8√3

Now since √3=1.732, you have

       x=4×1.732

         =6.928=7 (approximately )

and y=8×1.732

        =13.85=14 (approximately)

Worksheet for you to try :

Applications of right triangle trigonometry worksheet

Basic Right Triangle Trigonometry Worksheets

To solve these problems, you have to use the law of tangents, sines, and cosines as per the given adjacent side, opposite side and the hypotenuse. 

Example of finding the angle of a right angle triangle when the adjacent side and the hypotenuse are already given

Calculate the angle x of the right-angle triangle in the figure below. Here, the length of one side BC =3 and the hypotenuse AC=6.

Basic Right Triangle Trigonometry - Finding Angle

Since you have the length of the adjacent side of the angle C and the hypotenuse, you have to use the law of cosine.

So, cos x=adjacent side/hypotenuse

                  =BC/AC

                  =3/6

                  =1/2

Now, as we know cos 60 0 =1/2, so , x=60 0

Example of finding the angle of a right-angle triangle when the opposite side and the hypotenuse are already given

Calculate the angle x of the right-angle triangle in the figure below. Here the length of one side BC =14 and the hypotenuse AC=21.

Finding Angle - Opposite side and Hypotenuse

Since, you have the length of the opposite side of the angle A and the hypotenuse, you have to use the law of sine

So, sin x=opposite side/hypotenuse

                  =14/21

                  =2/3

                 =0.666

Now as sin 41.8 0 =0.666, so, x=41.8 0

Worksheets to try:

Basic Right triangle Trigonometry worksheet -1

Practice Worksheet – Right Triangle Trigonometry

Example of finding sin 45 degrees and cos 45 degrees of the right angle triangle in fraction form when all the three sides are given.

Right Triangle Trigonometry - Find angle when all three sides are given

Sin 45 0 =opposite side/hypotenuse

            = 4/7.2

            =40/72

            =10/18

            =5/9

Cos45 0 =adjacent side/hypotenuse

            = 6/7.2

            =60/72

            =10/12

            =5/6

Practice worksheet Right triangle trigonometry

Precalculus Right Triangle Trigonometry Worksheet

Example A swimmer is 210 meter below the surface of the ocean and begins to descend at an angle of 30 degrees from the vertical. How far will be the swimmer travel before he breaks the surface of the water.

Precalculus Right Triangle Trigonometry Problem

You know here Sin 30 0 =opposite side/hypotenuse

           So hyotenuse =210 ÷0.5

                                  =420

So, the swimmer travels 420 meter before he breaks the ocean surface.        

Precalculus Right triangles Trigonometry worksheet

Download              

Right Triangle Trigonometry – Angle of Elevation and Depression Worksheet

To solve the problems in the worksheet, you need to first know the concept of the angle of elevation and the angle of depression.

The angle of elevation -The angle formed when an observer looks at an object above his horizontal line of sight. For example, if you stand on a plateau and look at the peak of a nearby mountain, an angle of elevation is formed.

The angle of depression -The angle formed when an observer looks down at an object below his horizontal line of sight. For example, if you stand on a plateau and look at a house in the plains, an angle of depression is formed.            

Angle of Depression and Angle of Elevation

Example- A bird is sitting on an iceberg 100 feet above the water. If a sea lion in water is 220 feet from the base of the iceberg, find the angle of depression.

Find Angle of Depression - Problem with Solution

Let x is the angle of elevation that the sea lion at a distance of 220 meter from the base of the iceberg makes when he looks at the bird sitting on the iceberg at a vertical height of 100 meters.

From the above figure, it becomes apparent that tan x 0 =adjacent side /opposite side

                                                                                       =220/100

                                                                                       =11/5

                                                                             tan 66 0 =2.2

Now as tan 66 0 =2.2,you have angle of elevation x= 66 0

Next, we know that the sum of all three angles of a triangle equals to 180 0

So, the remaining angle will be =180 0 –(66 0 + 90 0 ) = 180 0 – 156 0 =24 0

Hence, the angle of depression = 90 0 – 24 0 =66 0

Example A 25 feet ladder leans against a house so that the base of the ladder is 7 feet from the base of the house. What will be the angle of elevation of the ladder.

                   

Find Angle of Elevation - Trigonometry Problem

cos x=adjacent side/hypotenuse

        =7/14

   So, angle of elevation of the ladder= 60 0  

Right triangles Trigonometry angle of elevation and depression worksheet

Special Right Triangle Trigonometry Worksheet

Example-Half of an equilateral triangle is often called “30-60” right or “30-60-90” triangle. Explain why it is called with that name?

Since, an equilateral triangle can be split into two right angle triangles with the remaining angles being 30 degrees and 60 degrees, half of an equilateral triangle is often called “30-60” right or “30-60-90” triangle.  Let us prove this with the help of the law of sine and cosine.                     

Special Right Triangle - Trigonometry Problem

Let ABC is an equilateral triangle with sides x, y and z where x=y=z.

Now you draw a perpendicular from vertex A on the side BC, you will have two right angle triangles-ABD and ACD with angle D=90 0 .

Next, as per the law of cosine, you know in the right-angle triangle ADC

cos C=adjacent side/hypotenuse

          =DC/AC

          =Half of the side z/y

         =y/2 ÷ y

         =1/2

Now from the trigonometry table, you know that cos 60 0 =1/2

So,      ∠C=60 0

Similarly, as per the law of sine, you know  that in the right-angle triangle ADC

Sin A=opposite side/hypotenuse

         = DC/AC

Now from the trigonometry table, you know that sin30 0 =1/2

So,     ∠A=30 0

Hence, you have in the right-angle triangle ACD, A=30 0 , C=60 0 , and D=90 0

Similarly, in the right-angle triangle ABD, A=30 0 , B=60 0 , and D=90 0

Special right triangles Trigonometry worksheet

Right Triangle Trigonometry Finding Missing Sides & Angles Worksheet

Right triangles Trigonometry finding missing sides angle worksheet

Right Triangle Trigonometry Word Problems Worksheet

Rright triangles Trigonometry word problems worksheet

Trigonometry Ratios in Right Triangles Worksheet

Trigonometry Ratios in right triangle worksheet

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Math Worksheets Land

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Working with Right Triangles Worksheets

This is the one of the geometric shapes that literally makes the construction of perfectly straight edges possible. Using the Pythagorean theorem, we can find missing sides of these shapes. As we advance into trigonometry, we will learn that you do not much information at all about these shapes to be able to determine all of the angles and lengths of sides. Something that people often do not realize is that if put a diagonal line across a rectangle and cut along that line, you have just created two right-angled triangles. Contractors use the property of geometry all day to create perfectly level and straight structures. This series of lessons and worksheets teach students how to complete figure out all measures on right triangles through a wide variety of techniques.

Aligned Standard: HSG-SRT.C.8

  • Find Opposite Step-by-Step Lesson - Given two sides, find the third of the right triangle.
  • Guided Lesson - In summer, I always think of problems in my head like number two.
  • Guided Lesson Explanation - These problems real help students get the concepts that are mystifying to lower level geometry students.
  • Practice Worksheet - This one took me a while. All nicely thought out real world problem set for you to work with.
  • Matching Worksheet - In real life if you took the time to think and solve problems like this, you would need to find a hobby.
  • Working with Right Triangles Worksheet Five Pack - All these problems have to visualized because they are in sentences.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

There are just so many different ways you can handle these problems.

  • Homework 1 - A triangle contains exactly one 90° angle. The other two angles must total exactly 90 degrees. The famous Pythagoras Theorem defines the relationship between the three sides of a right triangle.
  • Homework 2 - Jack saw a building that is 75 feet in height. The building casts a 30 foot shadow. What is the angle of elevation from the end of the shadow to the top of the building with respect to the ground?
  • Homework 3 - A right triangle's opposite side is 10 and the hypotenuse is 18. Find the value of normal base?

Practice Worksheets

Over the course of the practice I show two different methods for answering the problems.

  • Practice 1 - Find the value of normal opposite side?
  • Practice 2 - Mark drives 10 km due east of his home. Then he heads 12km north. What is the total distance that he has travelled from his house?
  • Practice 3 - Mr. Mike wants to purchase a square shaped table for his office. Table height is 6 feet. Mr. Mike ties a diagonal ribbon on the table. How long must be the ribbon?

Math Skill Quizzes

The first one is just with plain old triangles. The last two are all application word problems.

  • Quiz 1 - A right triangle has a opposite side that is 10 units in length and a hypotenuse that is 14 units. Find the value of base?
  • Quiz 2 - A road light is 40 feet in height and casts a shadow that is 15 feet long. What is the angle of elevation from the end of the shadow to the top of the road light with respect to the ground? This is assuming that the road light is 100% straight.
  • Quiz 3 - Alan has a square shaped television. The height of television is 8 inches. Alan wants to put a diagonal paper on the television. How long must the paper be?

Tips for Working with Right Triangles

Labeled Right Triangle

A right-angled triangle is one where one of the angles is 90 degrees. As you can see in the diagram to the right, that angle is often denoted by the presence of a square. There are a few unique features of these geometric shapes that you should be aware of. The longest side that is formed as a result of the right angle is opposite that right angle and called the hypotenuse. The altitude in a two-dimensional right triangle is the side that indicates height. The bottom side is referred to as the base. Depending on the orientation the two sides that are not the hypotenuse are interchangeable as result these sides are often referred to as legs. Since a triangle contains 180 degrees of internal angles, the sum of the measures of the legs must be 90 degrees.

The angles are often labeled which allows you to name the triangles. When naming triangles, we can pick any angle name them by labelling the angles in either a clockwise or counterclockwise direction. It does not which you pick as long as the angles fall in same consecutive order that they are found.

Working with right-angled triangles is relatively easier compared to other types of triangles. The reason behind this is simple. You always know the angles, and this can help solve many trigonometric word problems. One of the most common uses of right-angled triangles is the use of the Pythagoras theorem, which is Altitude 2 + Base 2 = Hypotenuse 2 . This allows you to find the measures of missing sides.

When working with right-angled triangles or solving problems that involve them, we can use the properties of sines, cosines, and tangents for determining many different missing sides or angles. Here are some other formulas that can be used with right-angled triangles to identify its unknown parts.

Sines: sin A = a/c, sin B = b/c | Cosines: cos A = b/c, cos B = a/c | Tangents: tan A = a/b, tan B = b/a

Let's just look at some of the cases where we don't know all the sides. Suppose we don't know the sides, but we are familiar with the other two sides. Using the Pythagoras theorem, we can easily identify the remaining two sides. If you know the measure of a side and angle, you can often determine all the others in this geometric environment which makes it a very handy shape to understand.

How Does This Apply to Real Life?

Understanding how to use and manipulate right triangles is one of the most important skills that covered in trigonometry. All of these geometric shapes consist of a single angle that measures ninety degrees. This allows use to use the Pythagorean theorem to our advantage to determine any unknown side or angle within the figure as long as we have a reference side or angle to work off of. In your everyday life you can use this to help achieve very similar things. The minute that you lean a ladder against a straight wall, you have created a right triangle. Want to know the height of the ladder, at what point it touches the wall, or the angle of the ladder, that can all be determined using the same exact math. You can use this math to determine the heights of building or natural structure in much the same way. When we are working with maps to locate areas or plot exact distances between objects, these figures can be pivotal to help you complete this. Anything that involves a coordinate system can be manipulated and better understood with the help of these figures. Mainly because if understand one measure you can learn a great deal about the system it is surrounded in.

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High school geometry

Course: high school geometry   >   unit 5.

  • Right triangle word problem
  • Angles of elevation and depression

Right triangle trigonometry word problems

  • Right triangle trigonometry review
  • Right triangles and trigonometry FAQ
  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

practice worksheet right triangle trigonometry

Right Triangle Trigonometry

Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

right triangle trigonometry

Problems & Videos

Solve the following right triangles, \(\textbf{1)}\) find the missing sides and angles. show answer the answer is \(m\angle d=48^{\circ},\,\,\, e\approx 10.8,\,\,\, f\approx 16.1\), \(\textbf{2)}\) find the missing sides and angles. show answer the answer is \(m\angle a\approx55^{\circ},\,\,\, a\approx 8.2,\,\,\, c\approx 5.74\) show work \(\text{solve for side } c\) \(\,\,\,\,\,\,\sin{\theta}=\frac{opposite}{hypotenuse}\) \(\,\,\,\,\,\,\sin{35^{\circ}}=\frac{c}{10}\) \(\,\,\,\,\,\,c=10\cdot\sin{35^{\circ}}\) \(\,\,\,\,\,\,c\approx 5.74\) \(\text{solve for side a}\) \(\,\,\,\,\,\,a^2+c^2=b^2\) \(\,\,\,\,\,\,a^2+(5.74)^2=(10)^2\) \(\,\,\,\,\,\,a^2+32.95=100\) \(\,\,\,\,\,\,a^2=67.05\) \(\,\,\,\,\,\,a=\sqrt{67.05}\) \(\,\,\,\,\,\,a\approx 8.2\) \(\text{solve for }m\angle a\) \(\,\,\,\,\,\,m\angle a + m\angle b + m\angle c = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a + 90^{\circ} + 35^{\circ} = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a + 125^{\circ} = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a = 55^{\circ} \), \(\textbf{3)}\) find the missing sides and angles. show answer the answer is \(m\angle a\approx20^{\circ},\,\,\, a\approx 1.09,\,\,\, b\approx 3.19\) show work \(\text{solve for side } b\) \(\,\,\,\,\,\,\sin{\theta}=\frac{opposite}{hypotenuse}\) \(\,\,\,\,\,\,\sin{70^{\circ}}=\frac{3}{b}\) \(\,\,\,\,\,\,b=\displaystyle\frac{3}{\sin{70^{\circ}}}\) \(\,\,\,\,\,\,b\approx 3.19\) \(\text{solve for side a}\) \(\,\,\,\,\,\,a^2+c^2=b^2\) \(\,\,\,\,\,\,a^2+(3)^2=(3.19)^2\) \(\,\,\,\,\,\,a^2+9=10.18\) \(\,\,\,\,\,\,a^2=1.18\) \(\,\,\,\,\,\,a=\sqrt{1.18}\) \(\,\,\,\,\,\,a\approx 1.08\) \(\text{solve for }m\angle a\) \(\,\,\,\,\,\,m\angle a + m\angle b + m\angle c = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a + 90^{\circ} + 70^{\circ} = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a + 160^{\circ} = 180^{\circ} \) \(\,\,\,\,\,\,m\angle a = 20^{\circ} \), \(\textbf{4)}\) express \(\cos{32^{\circ}}\) in terms of sine. show answer the answer is \(\sin{58^{\circ}}\) show work \(\,\,\,\,\,\cos(x)=\sin(90-x)\) \(\,\,\,\,\,\cos(32)=\sin(90-32)\) \(\,\,\,\,\,\cos(32)=\sin(58)\), \(\textbf{5)}\) express \(\sin{48^{\circ}}\) in terms of cosine. show answer the answer is \(\cos{42^{\circ}}\) show work \(\,\,\,\,\,\sin(x)=\cos(90-x)\) \(\,\,\,\,\,\sin(48)=\cos(90-48)\) \(\,\,\,\,\,\sin(48)=\cos(42)\), see related pages\(\), \(\bullet\text{ geometry homepage}\) \(\,\,\,\,\,\,\,\,\text{all the best topics…}\), \(\bullet\text{ right triangle trigonometry}\) \(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\), \(\bullet\text{ angle of depression and elevation}\) \(\,\,\,\,\,\,\,\,\text{angle of depression}=\text{angle of elevation}…\), \(\bullet\text{ convert to radians and to degrees}\) \(\,\,\,\,\,\,\,\,\text{radians} \rightarrow \text{degrees}, \times \displaystyle \frac{180^{\circ}}{\pi}…\), \(\bullet\text{ degrees, minutes and seconds}\) \(\,\,\,\,\,\,\,\,48^{\circ}34’21”…\), \(\bullet\text{ coterminal angles}\) \(\,\,\,\,\,\,\,\,\pm 360^{\circ} \text { or } \pm 2\pi n…\), \(\bullet\text{ reference angles}\) \(\,\,\,\,\,\,\,\,\) \(…\), \(\bullet\text{ find all 6 trig functions}\) \(\,\,\,\,\,\,\,\,\) \(…\), \(\bullet\text{ unit circle}\) \(\,\,\,\,\,\,\,\,\sin{(60^{\circ})}=\displaystyle\frac{\sqrt{3}}{2}…\), \(\bullet\text{ law of sines}\) \(\,\,\,\,\,\,\,\,\displaystyle\frac{\sin{a}}{a}=\frac{\sin{b}}{b}=\frac{\sin{c}}{c}\) \(…\), \(\bullet\text{ area of sas triangles}\) \(\,\,\,\,\,\,\,\,\text{area}=\frac{1}{2}ab \sin{c}\) \(…\), \(\bullet\text{ law of cosines}\) \(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{a}\) \(…\), \(\bullet\text{ area of sss triangles (heron’s formula)}\) \(\,\,\,\,\,\,\,\,\text{area}=\sqrt{s(s-a)(s-b)(s-c)}\) \(…\), \(\bullet\text{ geometric mean}\) \(\,\,\,\,\,\,\,\,x=\sqrt{ab} \text{ or } \displaystyle\frac{a}{x}=\frac{x}{b}…\), \(\bullet\text{ geometric mean- similar right triangles}\) \(\,\,\,\,\,\,\,\,\) \(…\), \(\bullet\text{ inverse trigonmetric functions}\) \(\,\,\,\,\,\,\,\,\sin {\left(cos^{-1}\left(\frac{3}{5}\right)\right)}…\), \(\bullet\text{ sum and difference of angles formulas}\) \(\,\,\,\,\,\,\,\,\sin{(a+b)}=\sin{a}\cos{b}+\cos{a}\sin{b}…\), \(\bullet\text{ double-angle and half-angle formulas}\) \(\,\,\,\,\,\,\,\,\sin{(2a)}=2\sin{(a)}\cos{(a)}…\), \(\bullet\text{ trigonometry-pythagorean identities}\) \(\,\,\,\,\,\,\,\,\sin^2{(x)}+\cos^2{(x)}=1…\), \(\bullet\text{ product-sum identities}\) \(\,\,\,\,\,\,\,\,\cos{\alpha}\cos{\beta}=\left(\displaystyle\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\right)…\), \(\bullet\text{ cofunction identities}\) \(\,\,\,\,\,\,\,\,\sin{(x)}=\cos{(\frac{\pi}{2}-x)}…\), \(\bullet\text{ proving trigonometric identities}\) \(\,\,\,\,\,\,\,\,\sec{x}-\cos{x}=\displaystyle\frac{\tan^2{x}}{\sec{x}}…\), \(\bullet\text{ graphing trig functions- sin and cos}\) \(\,\,\,\,\,\,\,\,f(x)=a \sin{b(x-c)}+d \) \(…\), \(\bullet\text{ solving trigonometric equations}\) \(\,\,\,\,\,\,\,\,2\cos{(x)}=\sqrt{3}…\), in summary…, right triangle trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of right triangles. a right triangle is a triangle with one right angle, and the side opposite the right angle is called the hypotenuse. the other two sides are called the legs of the triangle. the trigonometric functions are used to describe the relationships between the sides and angles of a right triangle. the three main trigonometric functions are sine, cosine, and tangent. these functions are often abbreviated as sin, cos, and tan, respectively. the sine function is defined as the ratio of the length of the side opposite an angle to the length of the hypotenuse \(\left(\frac{\text{opposite}}{\text{hypotenuse}}\right)\). the cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse \(\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)\). and the tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side \(\left(\frac{\text{opposite}}{\text{adjacent}}\right)\). soh cah toa is a popular way to remember these relationships. another one of the important tools in right triangle trigonometry is the pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. this can be written as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. to solve for the acute angles in right triangle trigonometry, it is often necessary to use the inverse trigonometric functions, which are the inverse of the sine, cosine, and tangent functions. these functions are abbreviated as \(\sin^{-1}\), \(\cos^{-1}\), and \(\tan^{-1}\), respectively. right triangle trigonometry is used in a variety of fields, including geometry, engineering, and physics. it is also a useful tool for solving real-world problems., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting, right triangle trigonometry is a branch of mathematics that deals with the study of triangles, specifically right triangles. a right triangle is a triangle in which one of the angles is a right angle (90 degrees). right triangle trigonometry is based on the principles of geometry and algebra, and it is used to find the lengths of the sides and the measure of the angles of a right triangle. it is a crucial tool for solving problems in various fields, such as engineering, physics, and architecture. right triangle trigonometry is often taught in high school math classes, usually in the geometry or algebra ii curriculum. it is an essential foundation for further study in mathematics and related fields. one common mistake students make when learning right triangle trigonometry is confusing the three primary trigonometric functions: sine, cosine, and tangent. these functions are used to relate the sides of a right triangle to the angles, and it is important to understand how to use them correctly. an interesting fact about right triangle trigonometry is that it was first developed by the ancient greeks, who used it to study the properties of triangles and to solve problems in geometry. the greek mathematician pythagoras is credited with discovering the famous pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. in addition to the pythagorean theorem, there are several other important theorems and formulas in right triangle trigonometry, such as the law of sines and the law of cosines. these theorems allow us to solve for unknown quantities in right triangles, even when we do not have a right angle. other related topics in mathematics that are closely connected to right triangle trigonometry include trigonometry in general, complex numbers, and vector calculus. these topics build on the concepts introduced in right triangle trigonometry and are often studied at the college level. in conclusion, right triangle trigonometry is a fundamental branch of mathematics that deals with the properties of right triangles. it is used in various fields and has a long history dating back to the ancient greeks. understanding right triangle trigonometry is essential for further study in mathematics and related fields. andy math 5 real world examples of right triangle trigonometry here are five real-world examples of right triangle trigonometry: surveying: surveyors use right triangle trigonometry to measure distances and angles on the land. for example, they may use a theodolite, a tool that measures angles in both the horizontal and vertical planes, to determine the elevation of a certain point. navigation: navigators and pilots use right triangle trigonometry to find their position and to determine the distance and direction to their destination. they use instruments like sextants, which measure the angle between two objects, and calculate their position using trigonometric formulas. construction: in construction, right triangle trigonometry is used to calculate the dimensions of buildings and other structures. for example, architects and engineers may use trigonometry to determine the slope of a roof or the height of a tower. sports: right triangle trigonometry is also used in sports, such as golf and baseball. golfers use trigonometry to calculate the distance to the hole and to determine the best club to use for a shot. in baseball, trigonometry is used to calculate the trajectory of a pitched ball and the distance it will travel. space exploration: right triangle trigonometry is essential for space exploration, as it is used to calculate the orbits of satellites and to navigate spacecraft. it is also used to determine the distance and size of celestial objects, such as planets and stars. andy math 5 other math topics that use right triangle trigonometry here are five other math topics that use right triangle trigonometry: trigonometry: right triangle trigonometry is a subfield of trigonometry, which is the study of triangles in general. trigonometry involves the study of the relationships between the sides and angles of triangles, and it includes concepts such as the sine, cosine, and tangent functions, which are used to relate the sides and angles of a right triangle. complex numbers: complex numbers are numbers that consist of a real part and an imaginary part. they can be represented in the form a + bi, where a and b are real numbers and i is the imaginary unit. complex numbers can be used to represent points in the complex plane, and trigonometry is used to perform geometric operations on these points. vector calculus: vector calculus is a branch of mathematics that deals with vector fields, which are functions that assign a vector to every point in space. vector calculus uses trigonometry to perform operations such as dot products, cross products, and gradient, divergence, and curl. differential equations: differential equations are equations that involve derivatives, which are used to describe how a function changes over time. trigonometry is often used to solve differential equations, especially in engineering and physics. fourier analysis: fourier analysis is a technique used to decompose a function into a sum of simpler periodic functions, called sine and cosine waves. trigonometry is used to perform fourier analysis, which is used in fields such as signal processing, image processing, and data compression. i've put out a lot of practice problems, notes and videos related to right triangle trigonometry on andymath.com. i hope it helps thank you.

practice worksheet right triangle trigonometry

Right Triangle Trigonometry Notes and Worksheets

These right triangle trigonometry notes and worksheets cover:

  • Intro to trig ratios
  • Sin, Cos, Tan of complementary angles
  • Finding a missing side
  • Finding a missing angle
  • Pythagorean Theorem (review)
  • Solving right triangles
  • Trig Ratios in similar triangles
  • Geometric mean
  • Application problems

Each topic has guided notes and 1-2 worksheets. There are 20 pages total + the answer keys.

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  1. Right Triangle Trigonometry Worksheets

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  6. 14 Basic Trigonometry Worksheet / worksheeto.com

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  1. pg#135| Chap#6 Area of triangle| Practice Questions| New Oxford Syllabus Primary Mathematics Book 5

  2. Trigonometry: Lecture 02

  3. Q 2, Trigonometry, Ex 8 1,Class 10, Maths

  4. Sec 2H-5.4c #3 Special Right Triangles Combined 23-24

  5. Worksheet [4]-Trigonometry 1st Secondary

  6. Worksheet [5]-Trigonometry 1st Secondary

COMMENTS

  1. PDF Right Triangle Trig Missing Sides and Angles

    ©5 n2K001 q2j RKZuzt ta Y DSJo sfdt 2w3aWr1ef YLzLECu.7 u 5A vlklw crbi gXhKtXsB grnezsfedrWvde5dM.z v GMmaYdte 2 OwuiAt0h q vI5nAf 2i4nCiFt2e m PAhlQgBeub hrOaz 62 e.e Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Right Triangle Trig.

  2. Right triangles & trigonometry

    Unit 1: Right triangles & trigonometry 700 possible mastery points Mastered Proficient Familiar Attempted Not started Quiz Unit test About this unit Can you find the length of a missing side of a right triangle? You most likely can: if you are given two side lengths you can use the Pythagorean Theorem to find the third one.

  3. PDF UNIT 8 RIGHT TRIANGLES NAME PER

    1. I can solve for the missing hypotenuse of a right triangle. 2. I can solve for the missing leg of a right triangle. 3. I can identify Pythagorean Triples. ASSIGNMENT: Introduction to Pythagorean Theorem Worksheet Grade: Block day, 1/9 - 10 Pythagorean Theorem, Converse, and Inequalities 4.

  4. Solve for a side in right triangles (practice)

    High school geometry > Right triangles & trigonometry > Solving for a side in a right triangle using the trigonometric ratios Solve for a side in right triangles Google Classroom You might need: Calculator B C = Round your answer to the nearest hundredth. 35 ∘ ? 6 C B A Show Calculator Stuck? Review related articles/videos or use a hint.

  5. Trigonometry Worksheets

    Trigonometry Worksheet Answer Page. Now you are ready to create your Trigonometry Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Trigonometry Worksheet will produce problems for solving right triangles. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th ...

  6. PDF Right Triangle Trigonometry Date Period

    Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Right Triangle Trigonometry Name_____ Date_____ Period____-1-Find the value of each. Round your answers to the nearest ten-thousandth. 1) csc ° 2.5593 2) tan 0.4663 Find the value of the trig function indicated. 3) csc

  7. Trigonometric ratios in right triangles (practice)

    Trigonometric ratios in right triangles. Google Classroom. β 4 5 3 C B A. Find tan ( β) in the triangle.

  8. Right Triangle Trigonometry Worksheets

    Applications of Right Triangle Trigonometry Worksheet To solve these problems, you will have to first learn the concept of the Pythagorean Theorem and the law of tangents. The Pythagorean Theorem - Is about the relationship between the three sides of a right-angle triangle.

  9. Right Triangle Trigonometry Worksheets

    Practice Worksheet We will put this skill to the test and see how many of those unknown angles we can figure out. Ten questions are provided. Review and Practice This worksheet reviews how to use the tangent of a given angle to solve for x. Six practice questions are provided. Quiz

  10. PDF RIGHT TRIANGLE TRIGONOMETRY

    Right Triangle Trigonometry Special Right Triangles Examples Find x and y by using the theorem above. Write answers in simplest radical form. 1. Solution: The legs of the triangle are congruent, so x =7. The hypotenuse is 2 times the length of either leg, so y =72. 2. Solution: The hypotenuse is 2 times the length of either leg, so

  11. PDF 9-Solving Right Triangles

    Q Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Solving Right Triangles Date_____ Period____ Find the missing side. Round to the nearest tenth. 1) 6 x 72° 2) x 6 73° 3) x 12 24° 4) x 12 37° ... 9-Solving Right Triangles Author: Mike Created Date:

  12. Right Triangle Trigonometry

    03:19. 30-60-90 Triangles - Special Right Triangle Trigonometry. The Organic Chemistry Tutor. 156. 04:38. Cool Pattern for Trig Special Angles. YourMathGal.

  13. Right Triangle Trigonometry Practice Teaching Resources

    Right Triangles - Sin Cos Tan (Soh Cah Toa) Trigonometry Riddle Practice Worksheet This is a 15 question right triangle worksheet that requires students to use sine, cosine and tangent to find the missing sides or the missing angles. It includes a riddle for the students to solve by solving the problems correctly. I have included an answer key as well. This is a great little assignment to use ...

  14. Working with Right Triangles Worksheets

    The first one is just with plain old triangles. The last two are all application word problems. Quiz 1 - A right triangle has a opposite side that is 10 units in length and a hypotenuse that is 14 units. Find the value of base? Quiz 2 - A road light is 40 feet in height and casts a shadow that is 15 feet long.

  15. Results for right triangle trigonometry worksheet

    Right Triangles - Sin Cos Tan (Soh Cah Toa) Trigonometry Riddle Practice Worksheet This is a 15 question right triangle worksheet that requires students to use sine, cosine and tangent to find the missing sides or the missing angles. It includes a riddle for the students to solve by solving the problems correctly.

  16. Right triangle trigonometry word problems (practice)

    Math > High school geometry > Right triangles & trigonometry Modeling with right triangles Right triangle trigonometry word problems Google Classroom You might need: Calculator Bugs Bunny was 33 meters below ground, digging his way toward Pismo Beach, when he realized he wanted to be above ground.

  17. Right Triangle Trigonometry

    A right triangle is a triangle with one right angle, and the side opposite the right angle is called the hypotenuse. The other two sides are called the legs of the triangle. The trigonometric functions are used to describe the relationships between the sides and angles of a right triangle.

  18. College Trigonometry Video Tutorial & Practice

    Textbook Question. In Exercises 21-28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −8 cos π/2 t. 129.

  19. PDF Trigonometry Worksheet T1

    Trigonometry Worksheet T1 - Labelling Triangles Label the sides of the triangles below with O for Opposite, A for Adjacent and H for Hypotenuse, Trigonometry Worksheet T2 - Sine, Cosine & Tangent Values ANSWERS (to 4 d.p.)

  20. Right Triangle Trigonometry Practice Worksheet

    Looking for right triangle trigonometry practice in Geometry? This SOH CAH TOA Worksheet is the perfect solution! All you need to do is print and copy for your students! This worksheet covers using SOH CAH TOA to find missing sides and angles, including some word problems.This SOH CAH TOA Practice...

  21. Right Triangle Trigonometry Notes and Worksheets

    These right triangle trigonometry notes and worksheets cover: Intro to trig ratios. Sin, Cos, Tan of complementary angles. Finding a missing side. Finding a missing angle. Pythagorean Theorem (review) Solving right triangles. Trig Ratios in similar triangles. Geometric mean.

  22. Trigonometry Practice Questions

    The Corbettmaths Practice Questions on Trigonometry. ... Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. ... Answers - Version 2. Practice Questions. Previous: Standard Form Practice Questions. Next: Similar Shapes Area/Volume Practice Questions. GCSE Revision Cards. 5-a-day Workbooks ...

  23. Polynomials

    Learn Polynomials with free step-by-step video explanations and practice problems by experienced tutors. Skip to main content. Precalculus Start typing, then use the up and down arrows to select an option from the list. ... Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle.