1. Use a graphing calculator to find tan 54°. Round to the nearest ten-thousandth.

2. Find mB to the nearest tenth of a degree if cos B = 0.8926 and B is an acute angle.

3. Refer to the figure. Find the value of x to the nearest tenth.

4. Refer to the figure. Find the value of x to the nearest tenth.

• angle of elevation

• angle of depression

• Solve problems involving angles of elevation.

• Solve problems involving angles of depression.

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

Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet, QS is 30.5 feet. Let x represent PQ.

Multiply both sides by x.

Divide both sides by tan

Simplify.

Angle of Elevation

Answer: The audience member is about 60 feet from the base of the platform.

A. A

B. B

C. C

D. D

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?

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

Read the ItemThe angle of depression between the ramp and the horizontal is Use trigonometry to find the height of the ramp.Solve the ItemMethod 1The ground and the horizontal level with the platform to which the ramp extends are parallel. Therefore,

since they are alternate interior angles.

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

Angle of Depression

Multiply each side by 3.

Simplify.

Angle of Depression

Method 2The horizontal line from the top of the platform to which the wheelchair ramp extends and the segment from the ground to the platform are perpendicular. So, and are complementary angles. Therefore,

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

Angle of Depression

Multiply each side by 3.

Simplify.

1. A

2. B

3. C

4. 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?

Indirect Measurement

Vernon 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.

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.

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

Indirect Measurement

Multiply each side by JL.

Divide each side by tan

Use a calculator.

Indirect Measurement

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

Multiply each side by KL.

Use a calculator.

Divide each side by tan

1. A

2. B

3. C

4. 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.