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Trigonometry Worksheets (Missing Sides)

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Trigonometry Worksheets

There are six sets of Trigonometry worksheets:

• Sin, Cos, Tan
• Sin & Cos of Complementary Angles
• Find Missing Sides
• Find Missing Angles
• Area of Triangle using Sine
• Law of Sines and Cosines

Find Missing Sides Worksheets

In these free math worksheets, students learn to find missing sides of a right triangle using Trigonometry.

There are two sets of Find Missing Sides worksheets: Find missing sides of triangles Missing sides word problems

How to find missing sides using Trigonometry?

To find missing side lengths using trigonometry when given a side and an angle in a right triangle, we can follow these steps:

Identify the known side and angle: Label the sides of the triangle as opposite, adjacent, and hypotenuse in reference to the given angle. Mark the known side length and angle on the diagram.

Choose the appropriate trigonometric ratio: Use the acronym SOH CAH TOA to determine which trigonometric ratio to use based on the known and missing sides: SOH: Sine = Opposite/ Hypotenuse CAH: Cosine = Adjacent/ Hypotenuse TOA: Tangent = Opposite/ Adjacent

Set up the equation and solve: Substitute the known values into the chosen trigonometric ratio. Solve for the missing side length using algebraic manipulation.

Here are some examples:

Example 1: Given a right triangle with a hypotenuse of 10 cm and an angle of 30°, find the length of the side opposite the angle.

Solution: Known side: Hypotenuse = 10 cm Known angle: 30° Needed side: Opposite Trigonometric ratio: SOH (because we are looking for the opposite side) Equation: sin(30°) = Opposite / 10 Solve: Opposite = 10 * sin(30°) = 5 cm

Example 2: Given a right triangle with an adjacent side of 6 cm and an angle of 45°, find the length of the hypotenuse.

Solution: Known side: Adjacent = 6 cm Known angle: 45° Needed side: Hypotenuse Trigonometric ratio: CAH (because we are looking for the hypotenuse) Equation: cos(45°) = 6 / Hypotenuse Solve: Hypotenuse = 6 / cos(45°) = 8.49 cm

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Trigonometry (Missing Sides) Worksheets .

More Trigonometry (Missing Sides) Worksheets

Printable (Answers on the second page.) Missing Sides Worksheet #1 Missing Sides Worksheet #2

Online Trigonometry (sine, cosine, tangent) Trigonometry (sine, cosine, tangent) Trigonometry (using a calculator) Inverse Trigonometry (using a calculator) Trigonometry (find an unknown side) Trigonometry (find an unknown angle) Using Sine Using Cosine Using Tangent Using Sine, Cosine or Tangent Trigonometry Applications Problems Law of Sines or Sine Rule Law of Sines Law of Cosines or Cosine Rule Law of Cosines

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Trigonometry Worksheets

Trigonometry worksheets promote an understanding of trigonometry concepts. Students can use these worksheets to improve their skills in solving trigonometric problems. The questions included in the worksheet are based on solving trigonometric identities, deriving trigonometry formulas, understanding trigonometry elements such sines, cosines, etc.

Benefits of Trigonometry Worksheets

Trigonometry finds use in several real life applications such as architecture, music, data analysis, etc. Hence, students must be well versed in the topic. This can only happen with clear concepts and immense practice that is provided by trigonometry worksheets.

As the scope of trigonometry is very vast, thus the worksheets have a gradual increase in the level of difficulty. This makes sure that a student doesn't get confused and can assimilate information effectively. Another added feature of these worksheets is that they are flexible, enabling students to work at their own pace.

Download Trigonometry Worksheet PDFs

They combine fun with studies so that students can have a holistic learning experience.These math worksheets should be practiced regularly and are free to download in PDF formats.

Visual maths worksheets, each maths worksheet is differentiated and visual.

Trigonometry Worksheets

Maths Worksheets / Trigonometry Worksheets

Trigonometry is a mathematical method used to define relations between elements of a triangle. Our maths trigonometry worksheets with answers will help your child or student to grasp and understand basic and more advanced ways of solving trigonometric equations. Our comprehensive resources include Pythagoras and trigonometry worksheets with answers, trigonometry area of triangle worksheets and transformations of trig graphs worksheets – all designed to make trigonometry fun and interesting.

Discovering Trigonometry (Investigation)

Trigonometry (A) Missing Lengths

Trigonometry (B) Missing Angles and Lengths

Trigonometry (C) Word Problems

Trigonometry (C) Word Problems (With Clues)

3D Trigonometry and Pythagoras (B)

Finding Exact Trig Values

3D Trigonometry – Cuboids

3D Trigonometry and Pythagoras (A)

Area of Triangles

Area of Triangles (With Clues)

Choosing the Correct Trig Rule

Sine Rule Cosine Rule and Area Mixed Exercise

The Cosine Rule

The Sine Rule

Trigonometric Graphs (A)

Trigonometric Graphs (B)

Using Exact Trig Values

Describing Transformations of Trig Graphs

Solving Trigonometric Equations

Transformations of Trig Graphs (A)

Transformations of Trig Graphs (B)

Printable Trigonometry Worksheets with Answers

Why is trigonometry important.

When learning about trigonometry, many students struggle to understand how it is relevant in real life.

Studying the properties of triangles and calculating missing angles can seem like an arbitrary task, but it actually has many applications in the real world. From astronomy, to aviation, medicine and more, trigonometry allows many industries to function.

Essential Knowledge for Future Scientists

A solid knowledge of trigonometry is essential for any student who aspires to work in a scientific discipline.

Students will need to master trigonometry at GCSE level in order to study A-Level maths and sciences, subjects which they will need to secure a university place for engineering, medicine, and the sciences. Although many computer applications perform trigonometric calculations automatically, all the staff working in these industries will have an excellent knowledge of trigonometry and use it regularly.

Nurture Students’ Transferable Skills

Even if students do not wish to pursue a career in these technical and scientific fields, practicing trigonometry questions helps them develop transferable skills valued by all employers.

Using Trigonometry improves students’ problem solving abilities and promotes critical thinking, skills which will prove useful throughout their studies and into adult life. Providing students with trigonometry worksheets helps to nurture these skills, allowing them to be successful not just at their maths exams but right the way through their career.

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Unit 1: Right triangles & trigonometry

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. But, what if you are only given one side? Impossible? Cue sine, cosine, and tangent, which will help you solve for any side or any angle of a right triangle.

Ratios in right triangles

• Getting ready for right triangles and trigonometry (Opens a modal)
• Hypotenuse, opposite, and adjacent (Opens a modal)
• Side ratios in right triangles as a function of the angles (Opens a modal)
• Using similarity to estimate ratio between side lengths (Opens a modal)
• Using right triangle ratios to approximate angle measure (Opens a modal)
• Right triangles & trigonometry: FAQ (Opens a modal)
• Use ratios in right triangles Get 3 of 4 questions to level up!

Introduction to the trigonometric ratios

• Triangle similarity & the trigonometric ratios (Opens a modal)
• Trigonometric ratios in right triangles (Opens a modal)
• Trigonometric ratios in right triangles Get 3 of 4 questions to level up!

Solving for a side in a right triangle using the trigonometric ratios

• Solving for a side in right triangles with trigonometry (Opens a modal)
• Solve for a side in right triangles Get 3 of 4 questions to level up!

Solving for an angle in a right triangle using the trigonometric ratios

• Intro to inverse trig functions (Opens a modal)
• Solve for an angle in right triangles Get 3 of 4 questions to level up!

Sine and cosine of complementary angles

• Intro to the Pythagorean trig identity (Opens a modal)
• Sine & cosine of complementary angles (Opens a modal)
• Using complementary angles (Opens a modal)
• Trig word problem: complementary angles (Opens a modal)
• Trig challenge problem: trig values & side ratios (Opens a modal)
• Trig ratios of special triangles (Opens a modal)
• Relate ratios in right triangles Get 3 of 4 questions to level up!

Modeling with right triangles

• Right triangle word problem (Opens a modal)
• Angles of elevation and depression (Opens a modal)
• Right triangle trigonometry review (Opens a modal)
• Right triangle trigonometry word problems Get 3 of 4 questions to level up!

The reciprocal trigonometric ratios

• Reciprocal trig ratios (Opens a modal)
• Finding reciprocal trig ratios (Opens a modal)
• Using reciprocal trig ratios (Opens a modal)
• Trigonometric ratios review (Opens a modal)
• Reciprocal trig ratios Get 5 of 7 questions to level up!

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Trigonometry Worksheets for High School

Explore the surplus collection of trigonometry worksheets that cover key skills in quadrants and angles, measuring angles in degrees and radians, conversion between degrees, minutes and radians, understanding the six trigonometric ratios, unit circles, frequently used trigonometric identities, evaluating, proving and verifying trigonometric expressions and the list go on...

List of Trigonometry Worksheets

Explore the trigonometry worksheets in detail.

Grasp and retain trigonometric concepts with ease employing these visually appealing charts for quadrants and angles, right triangle trigonometric ratio chart, trigonometric ratio tables, allied angles and unit circle charts to mention a few.

Identify the quadrant encompassing the terminal side of the angle with this set of quadrants and angles worksheets. Draw the indicated angle on the coordinate plane, measure the angles in the quadrant and represent as degrees and radians and a lot more.

Conversion of Degrees and Radians

Introduce the two ways to measure an angle, namely degrees and radians with this set of worksheets. Adequate worksheets are provided to assist in practicing prompt conversions of degrees to radians and vice-versa.

To specifically and accurately measure the size of an angle in degrees, it is further broken down into degrees, minutes and seconds. This worksheet stack consists of ample exercises to practice conversion between degrees, minutes and seconds.

Determine the reference angles in degrees and radians, find the coterminal angles for the indicated angles, and positive and negative coterminal angles with this assemblage of reference and coterminal angles worksheets.

Trigonometric Ratios | Right Triangle Trigonometry

Kick start your learning with these trig ratio worksheets. Identify the legs, side and angles, introduce the six trigonometric ratios both primary trig ratios and reciprocal trig ratios and much more with these trigonometric ratio worksheets.

Included here are fundamental identities like quotient, reciprocal, cofunction and Pythagorean identities, sum and difference identities, sum-to-product, product-to-sum, double angle and half angle identities and ample trig expression to be simplified, proved and verified using the trigonometric formulas.

Unit Circle Worksheets

Packed in these unit circle worksheets are exercises to find the coordinates of a point on the unit circle, determine the corresponding angle measure, use the unit circle to find the six trigonometric ratios and a lot more.

Trigonometric Ratios of Allied Angles

Allied angle worksheets here enclose exercises like finding the exact value of the trigonometric ratio offering angle measures in degrees or radians, evaluating trig ratios of allied angles and proving the trigonometric statements to mention just a few.

Evaluating Trigonometric Expressions

These worksheets outline the concept of evaluating trigonometric expressions involving primary, reciprocal and fundamental trigonometric ratios, evaluating expressions using a calculator, evaluate using allied angles and more!

Evaluating Trigonometric Functions Worksheets

With this set of evaluating trigonometric functions worksheets at your disposal, you have no dearth of practice exercises. Begin with substituting the specified x-values in trigonometric functions and solve for f(x).

Inverse Trigonometric Function Worksheets

Utilize this adequate supply of inverse trigonometric ratio worksheets to find the exact value of inverse trig ratios using charts and calculators, find the measure of angles, solve the equations, learn to evaluate inverse and the composition of trigonometric functions and a lot more.

Law of Sines Worksheets

Navigate through this law of sines worksheets that encompass an array of topics like finding the missing side and the unknown angles, solving triangles, an ambiguous case in a triangle, finding the area of SAS triangle and more.

Law of Cosines Worksheets

Incorporate the law of cosines worksheets to elevate your understanding of the concept and practice to find the missing sides of a triangle, finding the unknown angles (SAS & SSS), solving triangles and much more.

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

Reinforce the concept of principal solutions of trigonometric equations with this adequate supply of worksheets like solving linear trigonometric equations, solving trigonometric equations in quadratic form and much more.

General Solutions of Trig Equations Worksheets

Employ this assortment of general solutions of trigonometric equations worksheets that feature ample of exercises to hone your skills in solving different types of trigonometric equations to obtain the general solutions.

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Exact Values of Trigonometric Ratios: Worksheets with Answers

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SOHCAHTOA Worksheet and Answer Key

Students will practice identifying adjacent, opposite sides (and hypotenuse) in right triangles and they will practice writing Sine Cosine Tangent (SOHCAHTOA) relationships. This sheet has model problems worked out, step by step -- as well as, 20 scaffolded questions that start out relatively easy and end with some real challenges.

Example Questions

Ii. identify sides opposite, adjacent to angles.

III. Use SOHCAHTOA

Visual Aids

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Sine Cosine Calculator
• Arcsine Calculator

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