Five-Minute Check (over Lesson 8–4)

NGSSS

Then/Now

New Vocabulary

Example 1:Angle of Elevation

Example 2:Angle of Depression

Example 3:Use Two Angles of Elevation or Depression

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 0.6738

B. 0.7432

C. 0.8090

D. 1.3764

Use a calculator to find tan 54°.

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 63.2

B. 26.8

C. 18.4

D. 0.999

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

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 14.1

B. 17.4

C. 19.4

D. 21.3

Find x. Round to the nearest tenth.

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 9.5

B. 15.9

C. 23.7

D. 30.8

Find x. Round to the nearest tenth.

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 34.7

B. 43.8

C. 46.2

D. 52.5

Find x. Round to the nearest tenth.

Over Lesson 8–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Use a special right triangle to express sin 45° as a fraction.

A.

B.

C.

D.

LA.1112.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text.

MA.912.G.5.4 Solve real-world problems involving right triangles.

You used similar triangles to measure distances indirectly. (Lesson 7–3)

• Solve problems involving angles of elevation and depression.

• Use angles of elevation and depression to find the distance between two objects.

• angle of elevation

• angle 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 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

DISTANCE Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot?

Make a sketch of the situation.

Since are parallel, mBAC = mACD by the Alternate Interior Angles Theorem.

Angle of Depression

Let x represent the horizontal distance from the seal to the cliff, DC.

c = 52°; AD = 40, and DC = x

Multiply each side by x.

Angle of Depression

Answer: The seal is about 31 feet from the cliff.

Divide each side by tan 52°.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 19 ft

B. 20 ft

C. 44 ft

D. 58 ft

Luisa is in a hot air balloon 30 feet above the ground. She sees the landing spot at an angle of depression of 34. What is the horizontal distance between the hot air balloon and the landing spot to the nearest foot?

Use Two Angles of Elevation or Depression

DISTANCE 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.

Use Two Angles of Elevation or Depression

Understand ΔMLK and ΔMLJ are right triangles.The distance between the dolphins isJK or JL – KL. Use the right trianglesto find these two lengths.

Plan Because are horizontallines, they are parallel. Thus, andbecause they are alternate interiorangles. This means that

Use Two Angles of Elevation or Depression

Multiply each side by JL.

Divide each side by tan

Use a calculator.

Solve

Use Two Angles of Elevation or Depression

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

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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.