If we call the balloon point B, then in triangle PQB,
angle Q is 180-(69-32) = 143°
angle P is 56-32 = 24°
So, angle B is 13°
Now use the law of sines to find QB
QB/sin24° = 60/sin13°
Observers at P and Q are located on the side of a hill that is inclined 32° to the horizontal, as shown. The observer at P determines the angle of elevation to a hot-air balloon to be 56°. At the same instant the observer at Q measures the angle of elevation to the balloon to be 69°. If P is 60 m down the hill from Q, find the distance from Q to the balloon. (Round your answer to the nearest meter.)
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