1

What you will learn

How to evaluate inverse trigonometric functions

How to find missing angle measures How to solve right triangles

Objective: Section 5-5 Solving Right Triangles

2

Introduction

Sometimes when solving triangles, we know the trigonometric value of an angle but not the angle.

When solving these problems, we need to use the inverse of a trigonometric function (working backward from the ratio to the angle measure).

Objective: Section 5-5 Solving Right Triangles

3

Definitions

The inverse of the basic trigonometric functions:

Arcsine = inverse of sine (sin-1)Arccosine = inverse of cosine (cos-1)Arctangent = inverse of tangent (tan-1)

Objective: Section 5-5 Solving Right Triangles

4

Example

sin x = can be re-written as x = arcsin

The answer consists of all angles that have as the value of sine x.

2

3

2

3

2

3

Objective: Section 5-5 Solving Right Triangles

5

Example Problems Solve each equation.

A. Sin x = C. Tan x = 1

B. Cos x =

2

3

2

2

Objective: Section 5-5 Solving Right Triangles

6

More Examples Evaluate each expression. Assume all angles

are in Quadrant I.

A.

B.

)11

6tan(tan 1

)3

2cos(arcsin

Objective: Section 5-5 Solving Right Triangles

7

You Try Evaluate each expression. Assume that all

angles are in Quadrant I.

A.

B.

)5

4tan(cos 1

)5

2cos(arccos

Objective: Section 5-5 Solving Right Triangles

8

Finding Angle Measures If f = 17 and d = 32, find E.

You Try! If d = 28 and f = 21, find F.

F

DEf

ed

Objective: Section 5-5 Solving Right Triangles

9

Word Problem A security light is being installed outside a

loading dock. The light is mounted 20 feet above the ground. The light must be placed at an angle so that it will illuminate the end of the parking lot 100 feet away. What should the angle of depression be?

Objective: Section 5-5 Solving Right Triangles

10

Solving Right Triangles

Solve the triangle described.A. A = 33o, b = 5.8

B. a = 23, c = 45

A

B

C

a

b

c

Objective: Section 5-5 Solving Right Triangles

11

You Try Solve each triangle described. Round to

the nearest tenth.A. K = 40o, k = 26

B. j = 65, l = 55

K

JL

j

l

k

Objective: Section 5-5 Solving Right Triangles

12

Homework

Homework: page 309, 16-24 even, 28-32 even, 36-40 even, 44