Question

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

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