WarmUp Find the sin θ, cos θ, and tan θ.

25

60

65 θ

How do you solve right triangles?

Unit 3 Day 6

San Francisco

If you know the sine, cosine, or tangent of an acute angle measure, you can use the inverse

trigonometric functions to find the measure of the angle.

5cos

13 1 1cos ( ) co

5cos

13s

67.4

Calculating Angle Measures from

Trigonometric Ratios

Use your calculator to find each angle measure to the nearest tenth of a degree.

A. cos-1(0.87) B. sin-1(0.85) C. tan-1(0.71)

cos-1(0.87) 29.5° sin-1(0.85) 58.2° tan-1(0.71) 35.4°

Example 1

Inverse trig functions:

Ex 2: Use a calculator to approximate the

measure of the acute angle. Round to the

nearest tenth.

26.6° 20.5° 50.2°

1tan (0.5)m A 1sin (0.35)m A

1cos (0.64)m A

a. tan A = 0.5 b. sin A = 0.35 c. cos A = 0.64

Solving Right Triangles

Ex 3: Find the unknown measures. Round lengths to the nearest

hundredth and angle measures to the nearest degree.

Since the acute angles of a right triangle are complementary, mT 90° – 29° 61°.

RT2 = RS2 + ST2

(5.7)2 = 52 + ST2

Since the acute angles of a right triangle are complementary, mT 90° – 29° 61°.

, so ST = 5.7 sinR.

Ex 4: Solve the right triangle. Round decimals the nearest tenth.

3

2

90

AB

BC

AC

m A

m B

m C

Use Pythagorean Theorem to find c… 2 2 32 3

3.6

c

c

3.6 Use an inverse trig function to

find a missing acute angle…

1 3tan ( ) 56.3

2m A

Use Triangle Sum Theorem to

find the other acute angle…

90 56.3 33.7m B

56.3°

33.7°

Ex 5: You are hiking up a mountain peak. You begin hiking at a trailhead whose elevation is about 9400 ft. The trail ends near the summit at 14,255 ft. The horizontal distance between these two points is about 17,625 ft. Estimate the angle of elevation from the trailhead to the summit.

opposite side: 14,255ft-9,400ft 4,85= 5 ft

4855tan

17625A

1 4855tan ( )

17625

15.4

Ex 6: A monster truck drives off a ramp in order to jump onto a row

of cars. The ramp has a height of 14 feet and a horizontal length of 26 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.

14 ft

26 ft

14tan

26 1 14

tan ( )26

28.3

Homework:

Page 331-332 #7-13, 15, 35

Ex 3: Solve the right triangle. Round to the nearest tenth.

53

90

30

m Q

m R

m P

PQ

PR

QR

37°

18.1

24.0

Example 2:

a.

b.

17sin

240A 1 17

sin ( )240

4.1 Convert 20 ft to in

To minimize horizontal distance use the greatest possible ramp angle

8tan(4.76 )

x

96.1 in.x