An ant looks up to the top of a building at an angle of elevation of 32°. Then, the ant walks an additional 88 feet from the edge of the building. If the new angle of elevation from the ant to the top of the building is 22°, find the height of the building. Round the answer to the nearest tenth.

A.

100.6 feet

B.

125.4 feet

C.

145.2 feet

D.

189.8 feet

Question

Mathematics

Yandel Farley

17 October, 03:13

An ant looks up to the top of a building at an angle of elevation of 32°. Then, the ant walks an additional 88 feet from the edge of the building. If the new angle of elevation from the ant to the top of the building is 22°, find the height of the building. Round the answer to the nearest tenth.

A.

100.6 feet

B.

125.4 feet

C.

145.2 feet

D.

189.8 feet

+2

Answers (1)

Know the Answer?

Andrews · Answer 1

Measure of the angle that is opposite the line of 88 feet:

180° - (22° + 148°) = 10°

Using the Sine Law:

sin 10° / 88 = sin 22° / x

0.173648 / 88 = 0.3746 / x

x · 0.173648 = 88 · 0.3746

x = 189.84 ft

h - height of a building:

h / x = sin 32°

h = x · sin 32° = 189.84 · 0.529919 = 100.59987 ≈ 100.6 ft

Answer: A) 100.6 feet