right triangle triginometry

Right Triangle TriginometryA Stand-Alone Instructional Resource

Created by Lindsay Sanders

Standards & Objectives

Students in Mathematics II will be able to-• Discover the relationship of the trigonometric

ratios for similar triangles.• Explain the relationship between the

trigonometric ratios of complementary angles.• Solve application problems using the

trigonometric ratios.

Introduction• This project is a tutorial for learning how to solve

right triangles using basic trigonometry.• You will learn vocabulary, participate in mini-

lessons, and answer questions based on what you learned.

• You will need a scientific calculator or use an online scientific calculator

• At the end of this tutorial, there are links to online resources for right triangle trigonometry, including applets and games.

Vocabulary

• Hypotenuse- the longest side, opposite of the right angle

• Opposite side- the side opposite of the chosen angle

• Adjacent side- the side touching the chosen angle

hypotenuse

adjacent

opposite To learn more, please watch this video

Trigonometric Ratios

Sine Cosine

Tangent

Click on the trigonometric ratios below to learn more.

Sine• A trigonometric ratio (fraction) for acute angles that

involve the length of the opposite side and the hypotenuse of a right triangle, abbreviated Sin

length of hypotenuse ABSin A = =

A

B

C

opposite

hypotenuseClick for example

Click fortrig ratios

length of leg opposite A BC

Example 1Find Sin A.

A

B

C

2515

20

Sin A = =hypotenuseBC

Click fortrig ratios

=15

25

= 35

= 0.60

oppositeAB

Click forpractice

You try!Find Sin A.

A

B

C

53

45

28

Click fortrig ratios

Click foranother

(a) = 0.62 2845

(b) = 0.532853

(c) = 0.85 4553

(d) = 1.89 5328

No this ratio is opposite over adjacent

No this ratio is adjacent over hypotenuse

No this ratio is hypotenuse over opposite

Yes this ratio is opposite over hypotenuse

Back to example

You try!Find Sin B.

A

B

C

24 26

10

Click fortrig ratios

(a) = 0.42 1024

(b) = 0.92 2426

(c) = 2.40 2410

(d) = 0.391026

No this ratio is opposite over adjacent

No this ratio is adjacent over opposite

No this ratio is adjacent over hypotenuse

Yes this ratio is opposite over hypotenuse

Back Click forCosine

Cosine• A trigonometric ratio for acute angles that involve

the length of the adjacent side and the hypotenuse of a right triangle, abbreviated Cos

length of hypotenuse ABCos A = =

A

B

C adjacent

hypotenuseClick for example

Click fortrig ratios

length of leg adjacent A AC

Example 2Find Cos A.

A

B

C

2515

20

Cos A = =hypotenuse

25

Click fortrig ratios

=20

AB

=54

= 0.80

adjacent AC

Click forpractice

You try!Find Cos A.

A

B

C

37 35

12

Click fortrig ratios

(a) = 0.32 1237

(b) = 0.95 3537

(c) = 2.92 3512

(d) = 0.341235

No this ratio is adjacent over opposite

No this ratio is opposite over adjacent

No this ratio is opposite over hypotenuse

Yes this ratio is adjacent over hypotenuse

Back to example

Click foranother

You try!Find Cos B.A

B

C

85

36

77

Click fortrig ratios

(a) = 0.42 3685

(b) = 0.47 3677

(c) = 0.91 7785

(d) = 1.108577

No this ratio is hypotenuse over adjacent

No this ratio is opposite over hypotenuse

No this ratio is opposite over adjacent

Yes this ratio is adjacent over hypotenuse

Back Click forTangent

Tangent• A trigonometric ratio for acute angles that involve

the length of the opposite side and the adjacent side of a right triangle, abbreviated Tan

length of leg adjacent ACTan A = =

A

B

C adjacent

Click for example

opposite

Click fortrig ratios

length of leg opposite A BC

Example 3Find Tan A.

A

B

C

2515

20

Tan A = = adjacent

=

Click fortrig ratios

AC

2015

=43

= 0.75

opposite BC

Click forpractice

Back

You try!Find Tan A.

A

BC

58

40

42

Click fortrig ratios

(a) = 1.05 4240

(b) = 0.72 4258

(c) = 0.69 4058

(d) = 0.954042

No this ratio is opposite over hypotenuse

No this ratio is adjacent over opposite

No this ratio is adjacent over hypotenuse

Yes this ratio is opposite over adjacent

Back Click foranother

You try!Find Tan B.

A

B

C12

915

Click fortrig ratios

(a) = 1.33 12 9

(b) = 0.60 915

(c) = 0.801215

(d) = 0.75 912

No this ratio is opposite over hypotenuse

No this ratio is adjacent over opposite

No this ratio is adjacent over hypotenuse

Yes this ratio is opposite over adjacent

Back Click to go on

Solving for a Side Length

In order to solve for x, you will need to use one of the trigonometric ratios you just learned about!

52x

42˚Click fortrig ratios

Click for example

Example 4Solve for x.

52x

42˚

Step 1. Decide what type of sides are given.

x – opposite52 – hypotenuse

Step 2. Decide what trig function to use.

Sine! It is opposite over hypotenuse!

Step 3. Set up the ratio and solve for x.

Sin 42˚ =

x

52Multiply both side by 52· 5252 ·Put 52 · sin 42 in calculator

34.8 = x

Click forpractice

Click fortrig ratios

Back

You try!Solve for x.

16

x

39˚

Click foranswer

Click fortrig ratios

Back

x = 10.1answer:

Click foranother

Click fortrig ratios

Back

You try!Solve for x.

10

x

31˚

Click foranswer

Click fortrig ratios

Back

x = 8.6answer:

Click foranother

Click fortrig ratios

Back

You try!Solve for x.

23

x

44˚

Click foranswer

Click fortrig ratios

Back

x = 22.2answer:

Click formore

Click fortrig ratios

Back

For more information…

@Home Tutor – Right Triangle Trig

YourTeacher – Solving for sides using Trig video

Right Triangle Calculator and Solver

This Stand Alone Instructional Resource was created using PowerPoint. All sounds are also from PowerPoint. Information, definitions, and examples

were adapted from in McDougall Littell’s Mathematics 2 textbook. Click to start over