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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

Verified Answer :

HomertheGenius

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

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