Question

The angle of depression from the hot-air balloon to the car is 32°.

How high is the hot-air balloon flying?
Give your answer to 2 s.f.

Answer 1

3500 ft

Explanation:

You want the height of a balloon that is 6600 ft from a car at an angle of depression of 32°.

Sine

The geometry can be modeled by a right triangle with hypotenuse 6600 ft, where the height of the balloon is opposite the 32° angle. The relevant trig relation is ...

Sin = Opposite/Hypotenuse

Opposite = Hypotenuse · Sin

height = (6600 ft)·sin(32°) ≈ 3497 ft

Rounded to 2 significant figures, the result is ...

The hot-air balloon is flying at a height of about 3500 feet.

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