1. find the sin b, cos b, and tan b. d.n.a. 2. find the value of x

1. Find the sin B, cos B, and tan B.

D.N.A.

6

B

A

C

5

11

2. Find the value of x.

12

B

A

14

x C

Find x. Round to the nearest tenth.

41

B

A

451)

x

C 15

B

A15

x

C

34B

A17

xC

2)

3)

8 – 5: Angles of Elevation and Depression

pp. 464 - 470

• angle of elevation

• angle of depression

• Solve problems involving angles of elevation.

• Solve problems involving angles of depression.

Standard 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. (Key)

Angle of Elevation

CIRCUS ACTS At the circus, a person in the audience at ground level watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat is 27°?

Make a drawing

Angle of Elevation

Make a drawing

= Opposite

Adjacent =

S o:h C a:hT o:a

9595095

530

5305095

530

1

5095

530

..

.

..

..

.

adj.

opp.27 Tan

x

xx

x

A. A

B. B

C. C

D. D

DIVING At a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top of the diver’s head, what is the camera’s angle of elevation to the nearest degree?

Camera

Diver = 6’

Platform height = 32’

Pool width = 50’

Opp = 38’

Adj = 45’

Make a drawing

S o:hC a:hT o:a

40

8391.0

8444.0

45

38

xm

x

x

Tan

adj.

opp. Tan

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

A. 37°

B. 35°

C. 40°

D. 50°

DIVING At a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top of the diver’s head, what is the camera’s angle of elevation to the nearest degree?

Angle of Depression

mx

x

5137431

1010.

.42 cos

1042 Cos

hyp

adj.42 Cos

adj.

hyp.

From her treehouse, Joan can look directly into her bedroom window. The angle of depression from the treehouse to the base of her house is . The tree is 10 meters from the base of the house. How far is the treehouse from the base of the house?

42

A wheelchair ramp is 3 meters long and inclines at 6°. Find the height of the ramp to the nearest tenth of a centimeter.

A 0.3 cm B 31.4 cm C 31.5 cm D 298.4 cm

Angle of Depression

Opposite xHypotenuse

31045310450

3)(.

3.

hyp

opp6 Sin

xx

Answer: The height of the ramp is about 0.314 meters, or 0.314(100) = 31.4 centimeters. The answer is B.

Multiply each side by 3.

Simplify.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 145 ft

B. 628 ft

C. 359 ft

D. 285 ft

A roller coaster car is at one of its highest points. It drops at a 63° angle of depression for 320 feet. How long of a vertical distance was the drop?

• Homework:

• pp 466 – 470, problems 1 – 10, 27, and 29 – 35

Indirect MeasurementVernon is on the top deck of a cruise ship and observes two dolphins following each other directly away from the ship in a straight line. Vernon’s position is 154 meters above sea level, and the angles of depression to the two dolphins are 35° and 36°. Find the distance between the two dolphins to the nearest meter.

x

154

35

Indirect Measurement ΔMLK and ΔMLJ are right triangles. The distance between the dolphins is JK or JL – KL. Use the right triangles to find these two lengths.

. and 35MKLm

Because are horizontal lines, they are parallel. Thus, and because they are alternate interior angles. This means that 36MJLm

Indirect MeasurementVernon is on the top deck of a cruise ship and observes two dolphins following each other directly away from the ship in a straight line. Vernon’s position is 154 meters above sea level, and the angles of depression to the two dolphins are 35° and 36°. Find the distance between the two dolphins to the nearest meter.

x

154

35

x

154

35

mx

x

x

..

.

15435 Tan

942197002

154

1547002

219.94m

x m

36

154

y

36

154

y

my

y

y

..

.

15436 Tan

982117265

154

1547265

219.93 m

211.98 m

Answer: The distance between the dolphins is JK – KL. JL – KL ≈ 219.93 – 211.96, or about 8 meters.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 14 ft

B. 24 ft

C. 37 ft

D. 49 ft

Madison looks out her second-floor window, which is 15 feet above the ground. She observes two parked cars. One car is parked along the curb directly in front of her window, and the other car is parked directly across the street from the first car. The angles of depression of Madison’s line of sight to the cars are 17° and 31°. Find the distance between the two cars to the nearest foot.