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.
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 .
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 :
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.
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.
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:
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.
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
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.
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.
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.
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.
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.
cos x=adjacent side/hypotenuse
=7/14
So, angle of elevation of the ladder= 60 0
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.
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
Right Triangle Trigonometry Finding Missing Sides & Angles Worksheet
Right Triangle Trigonometry Word Problems Worksheet
Trigonometry Ratios in Right Triangles Worksheet
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Trigonometric Identities
Trigonometric Identities Problems & Solver Worksheet in PDF Format
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Get the trigonometry worksheets here and begin your learning of the trigonometry functions today. Here in the article, we are going to provide our readers with the printable template of the trigonometry worksheet.
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Trigonometry Worksheets
This worksheet will help our readers in providing the proper study material of trigonometry. They can subsequently use the material to get a better understanding of how trigonometry works.
Trigonometry is that branch of mathematics that comes in the geometry domain. The main purpose of trigonometry is to deal with the right-angle triangle. For instance, with trigonometry, you can figure out the total area of the triangle.
Other than the geometric domain the trigonometry is useful in serving the other objectives as well. It’s highly useful in the domain of engineering, science, and even in navigation. Trigonometry is also used in the algorithm of modern computer devices in the IT sector.
Today the most computers provide the values of trigonometry functions. It makes it easier for the users as they don’t have to refer to the trigonometry table to find the values of functions.
Trig Equation Worksheet
Well, the trigonometry worksheet is probably the best way of conducting the daily practice of trigonometry-based questions. With these questions, our guests and readers can have a decent understanding of trigonometric questions.
If you have just begun studying trigonometry then we highly recommend you the trigonometry worksheet. In this worksheet, you will find some of the standard questions from early trigonometry. Most of these questions are based on the simple concept of triangle measurement.
For instance, you will be asked to provide the overall area of the triangle for yourself. In a similar manner, you may also need to provide the missing angle area of the triangle. Furthermore, the worksheet also compromises the questions based on the trigonometry equation and inverse trigonometric functions as well.
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Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.
(This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)
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Here is a graphic preview for all of the Trigonometry Worksheets . You can select different variables to customize these Trigonometry Worksheets for your needs. The Trigonometry Worksheets are randomly created and will never repeat so you have an endless supply of quality Trigonometry Worksheets to use in the classroom or at home. We have Trigonometric Ratios, Inverse Trigonometric Ratios, Solving Right Triangles, and Multi-Step Problems Worksheets for your use. Our Trigonometry Worksheets are free to download, easy to use, and very flexible.
These Trigonometry Worksheets are a great resource for children in 5th, 6th Grade, 7th Grade, and 8th Grade.
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Trigonometric Ratios Worksheets This Trigonometry Worksheet will produce trigonometric ratio problems. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th Grade.
Inverse Trigonometric Ratios Worksheets This Trigonometry Worksheet will produce inverse trigonometric ratio problems. You may select the number of sides given for the problems. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th Grade.
Solving Right Triangles Worksheets 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 Grade.
Multi-Step Trigomometric Worksheets This Trigonometry Worksheet will produce multi-step trigonometric problems. This worksheet is a great resource for the 5th Grade, 6th Grade, 7th Grade, and 8th Grade.
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Right Triangle Trigonometry Worksheet with Answers
Identifying a right triangle is a piece of cake. It is a triangle where one of its interior angles measures 90° and the side opposite to that angle is its longest side – the hypotenuse. However, let’s not focus on how it looks like and dig deeper unto the measures of its sides and the trigonometric functions coined with it!
What is the “ Right Triangle Trigonometry Worksheet with Answers ”?
Right Triangle Trigonometry Worksheet is a Math worksheet that is intended for learners to know more about trigonometry using their previous knowledge about right triangles. This will help them find the unknown lengths of the sides of a right triangle through Pythagorean theorem, learn more about the trigonometric functions, and solve real-life problems using right triangle trigonometry. The worksheet also includes the answers for the given problems which the users may use to check if they have solved the worksheet correctly.
What is Trigonometry?
Trigonometry is a branch of Mathematics which deals with the calculations of the lengths and angles of triangles using trigonometric functions – tangent, sine, and cosine ratios.
Instructions on how to use the “ Right Triangle Trigonometry Worksheet with Answers ”
Use this Math worksheet to know about the concept of right triangle trigonometry, its application in real-life problems, and how to solve them accurately. After the lesson, different activities are given to check your understanding with the concept. A real-life problem is also given to check if you know how to properly apply the concept in realistic situations. At the end of each activity, answers are given to assess your performance about the lesson.
Identifying triangles specifically right triangles is an easy thing to do, but finding the lengths of the sides and unknown measurements of its angles might be confusing for some who have not yet mastered the right triangle trigonometry. With the help of this worksheet, you will not just learn but rather become a master of this concept.
Let’s get to know what a right triangle is!
Right triangles are triangles with one of its interior angles measuring to 90°, its longest side is the side opposite to the right angle which is also called the hypotenuse. The sides adjacent to the right angle are the height and the base.
The Pythagorean Theorem
According to this theorem, for every right triangle, the sum of the squares of both legs – base and height, is equal to the square of the hypotenuse.
Calculating the Measurement of an Unknown Side of a Right Triangle Using Pythagorean Theorem
In the illustration above, both the sides adjacent to the right angle which are the legs are given. The unknown value is the side opposite to the right angle, which means that we’re solving for the hypotenuse.
Step 2. Apply the Pythagorean Theorem.
Step 3. Substitute the given values to the Pythagorean theorem and solve for the unknown variable.
Here are the formulas using Pythagorean theorem if any of the legs or hypotenuse is unknown:
Trigonometric Functions
If the measurements of the sides of the right triangle are known, all trigonometric functions can be calculated.
What are trigonometric functions?
These are functions of an angle expressed in terms of the ratios between the pairs of sides of a right triangle; this includes the sine, cosine, tangent, cosecant, secant, and cotangent.
Easy Way to Remember the Trigonometric Functions
And yes! As you have noticed, the second column is just the reciprocal of the trigonometric functions in the first column. The reciprocals of sine, cosine, and tangent are cosecant, secant, and cotangent, respectively.
Calculating Trigonometric Functions Given the Measurements of the Triangle’s Sides
Step 1. Identify the given values.
Hypotenuse is 10 cm, the side adjacent to the angle is 8 cm, and the side opposite to the angle is 6 cm.
Calculating Unknown Angle Measurement Using the Trigonometric Functions
Step 1: Identify what trigonometric function to use.
Since we are given the measurements of the opposite side and the hypotenuse, then we can use SOH. Sine is equal to opposite over hypotenuse.
Step 2. Substitute given values to the formula.
Step 3. Solve for the value of angle x.
The measurement of angle x is 36.87°.
Instructions: Consider the right triangles below. Solve for the measurement of the unknown side length using Pythagorean Theorem.
Answers to Activity 1
Solution:
- Find the measurement of the side opposite to angle B.
- Cosecant =
- Secant =
- Cotangent =
Answers to Activity 2
Find the measurements of angle A and B.
Answers to Activity 3
Since all the lengths of the sides of the triangle are given, any of the six trigonometric functions can be used.
Angle A measures 36.87 degrees and Angle B measures 53.13 degrees.
Real-Life Problem
Instructions: Solve the problem by applying your knowledge about right triangle geometry in a realistic situation.
Ryankane wants to create a ramp for his toy car but doesn’t know the exact length of the ramp he should be using. He already knows the steepness of the end of the ramp from the floor and the distance from the floor starting point to the floor end point. Help Ryankane solve for the length of the ramp.
Real-Life Problem Answer
Ryankane wants to create a ramp for his toy car but doesn’t know the exact length of the ramp he should be using. He already knows that the steepness of the end of the ramp from the floor is 7 cm and the distance from the floor starting point to the floor end point is 8 cm. Help Ryankane solve for the length of the ramp.
Illustrating the given problem,
Ryankane’s ramp should be approximately 10.63 centimeters.
You can download this worksheet here.
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Solving Triangles Worksheets
Basic comprehension of sine law and cosine law is a prerequisite to solve these exercises that are categorized into different topics. Our printable solving triangles worksheets are packed with practice problems to assess high school student's understanding in the law of sines and the law of cosines. Access some of these worksheets for free!
Solve - Type 1
Review the law of sines and the law of cosines with this assortment of worksheets. Help high students understand how to use both the laws in solving triangles.
Solve - Type 2
Implement either the sine law or the cosine law to solve the triangles featured in type 2 pdf worksheets. Test your comprehension of these laws by solving the triangles with the given set of measurements.
Find the Area of a Triangle
Read the triangle and use the appropriate Sine or Cosine formula to figure out the measurements that are required to find the area. Then substitute your values in Area = 1/2 ab sin c to determine the area of the triangle.
Solve - Given Area of a Triangle
Gain proficiency in trigonometry with this printable batch of advanced worksheets. Solve each triangle by utilizing the formulas of sine law, cosine law and area of a triangle.
Navigate through our enormous supply of worksheets to find the missing side, determine the unknown angle, find the area of SAS triangle and many more by applying the law of sines.
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Law of cosines is an important formula, used in solving triangles (except right-angled triangles). Download this wide array of the law of cosines pdf worksheets to find the unknown angle or missing side of each triangle.
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Trigonometry Worksheet T3 - Calculating Sides Work out the sides labelled. Questions 1 and 2 require Sine, questions 3 and 4 require Cosine, question 5 and 6 require Tangent. The rest …. you will need to work out which to use and how! (Worksheet T1 may help you!!) 1. 7. 2. 8. 3. 9. 4. 10. 5. 11. 6. 12.
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Solving Triangles Worksheets Access this huge collection of solving triangles worksheets to comprehend the topics like solving triangles, finding the area of the triangle, solving the triangle using the given area and much more worksheets are included. Principal Solutions of Trig Equations Worksheets
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
Trigonometry Worksheets This worksheet will help our readers in providing the proper study material of trigonometry. They can subsequently use the material to get a better understanding of how trigonometry works. Trigonometry is that branch of mathematics that comes in the geometry domain.
Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle) Law of Sines Ambiguous Case of the Law of Sines Law Of Cosines Sine, Cosine, Tangent Worksheets SOHCAHTOA
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 Grade. Multi-Step Trigomometric Worksheets This Trigonometry Worksheet will produce multi-step trigonometric problems.
These trig ratio worksheets feature exercises to identify the legs, side and angles, introduce the six trigonometric ratios, find the indicated sides and much more. Access some of these worksheets for free! Exclusive Trigonometric Ratios Worksheets » Primary Trigonometric Ratios » Reciprocal Trigonometric Ratios
©2 H2I001 X1g CKrubt Ea5 SPo 0fSt 1w8aPrVeK dLuLiC E.r Z 6A3lslM 6r wi2g ShNtos j ir Je CsYe0r QvAe9dD. 2 K FM BaTdie G xwZimt ohH xIKn9f ti6nGi8t 2ez qA Rl7g 1ewbDrga4 02 S.9 Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Right Triangle Trig. - Evaluating Trig.
Evaluating Trigonometric Functions Vocabulary Theta ( ) - A variable used in trigonometry to represent the measure of an acute angle Adjacent Side - The side of the right triangle that is next to angle theta but not the hypotenuse Opposite Side - The side of the right triangle that is across from theta Angle of Elevation = Angle of Depression
Use the sin function to find a length or an angle in a right-angled triangle. Cos - find angle Use the cos function to find an angle in a right-angled triangle. Cos - find length Use the cos function to find a length in a right-angled triangle. Cos - mixed problems Use the cos function to find a length or an angle in a right-angled triangle.
Trigonometry and Area Date_____ Period____ Find the area of each figure. Round your answer to the nearest tenth. 1) 6 cm 8 cm 87° 2) 5 in 6 in 140° 3) 3 yd 8 yd 98° 4) 7 in 4 in 96° 5) A triangle with two sides that measure 6 yd and 2 yd with an included angle of 10°. 6) A triangle with two sides that measure 6 m and
Calculating Trigonometric Functions Given the Measurements of the Triangle's Sides Suppose we are to find the values of tangent and secant given the figure below: Step 1. Identify the given values. Hypotenuse is 10 cm, the side adjacent to the angle is 8 cm, and the side opposite to the angle is 6 cm. Step 2.
Trig Double Triangles. Displaying all worksheets related to - Trig Double Triangles. Worksheets are Trig cheat, Trigonometry packet geometry honors, Gettin triggy wit it soh cah toa, Grade 11 general mathematics trigonometry, Trigonometry word problems, Trigonometry laws and identities, Real world trigonometry surveying, Trig substitution.
Worksheet 33 Trigonometry. Trig Ratios to fin missing lengths and angles together with. It can accept all the ratios right triangles and special trigonometric ratios and overlay a right triangle trigonometry worksheet! Use the definitions of lettuce three trig ratios to gold each statement. Pages from ngrb-0701-5pdf.
Area of a Triangle Using Sine We can use sine to determine the area of non-right triangles. This formula is derived from the area of a triangle formula, A=1/2Bh For any triangle ABC with side a opposite A, side b opposite B and side c opposite C, height h is represented by a line perpendicular to the base of the triangle. If SAS is
Our printable solving triangles worksheets are packed with practice problems to assess high school student's understanding in the law of sines and the law of cosines. Access some of these worksheets for free! Select the Measurement Units U.S. Customary Units Metric Units Solve - Type 1
Trigonometry: Area of any Triangle Video 337 on Corbettmaths Question 4: Find the length of the missing side in each of these triangles. Give each answer to one decimal place. (a) (b) (c) Question 5: Find the size of the missing acute angles below. Give each answer to one decimal place. (a) (b) (c)
Using Trigonometry to Find Angle Measures Date_____ Period____ Find each angle measure to the nearest degree. 1) tan A = 2.0503 2) cos Z = 0.1219 ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Trigonometry to Find Angle Measures
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