Unit 6 Lesson 6b Trigonometric Ratios

CCSSG-SRT 6: Understand that by

similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT 7: Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Lesson Goals• Use Trigonometric Ratios to

find missing side lengths in triangles.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Using Trigonometric Ratios

Trigonometric Ratios can be used to find missing side lengths.

1. Determine which trig ratio to use (sin, cos, tan).2. Write an equation with the given values 3. Find the value of the ratio on a trigonometric chart or scientific calculator.4. Solve the equation.

Example

13x opp

hyp

sin 3413x

34o

13x

Find .x

34o

13x

Example

13x opp

hyp

sin 3413x

Find .x

0.559213x

7.3x

ExampleFind .x

20x opp

adj

tan 5120x

1.234920x

24.7x 51o

20

x

Which trig ratio should be used to find ?x

You Try

40o

10x10x adj

hyp

cos 40

You TryWrite the equation needed to find .x

5x opp

adj

tan 705x

2.74755x

70o

5

x

You Try(this one is tricky)Find . x 9 adj

x hyp

9cos50x

90.6428x

0.6428 9x

14x

50o

9

x

ExampleFind the area of the triangle.

8h opp

hyp

sin 608h

0.8668h

6.928 h12A bh

60o

8 m

h

12 m

12 12 6.928A

241.6 mA

DefinitionAngle of Elevation

The angle created when looking at something high and a horizontal line.

DefinitionAngle of Depression

The angle created when looking at something low and a horizontal line.

ExampleWhile visiting the Pigeon Point Lighthouse, you wonder how tall the lighthouse is. Standing 100 feet from the base of the lighthouse, you discover that the angle of elevation is 49o. Use a trigonometric ratio to find the height.

tan oppadj

100 ft49o

The lighthouse is about 115 feet tall.

h115x

tan 49100h

1.1503100h

Summary

SOHCAHTOA is one way to remember the three basic trigonometric ratios. How will you remember the correct ratio for sine, cosine, and tangent?

What is a trigonometric identity?

How are trigonometric ratios used?

Today’s Assignment p. 563: 28 – 38 e, 41, 49, 51