Answer:
65.9 ft
Explanation:
The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.
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third angle
The sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...
angle C = 180° -75° -60° = 45°
ground distance
Then the distance between Amaya and Rochelle (c) is ...
c/sin(C) = r/sin(R)
c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)
c ≈ 65.8846
Amaya and Rochelle are about 65.9 feet apart.