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45 votes
From a hot-air balloon, Enola measures a 22 degrees angle of depression to a landmark that’s 310 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.

User Skyel
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1 Answer

20 votes
20 votes

Answer:

125.25 ft

Explanation:

The geometry of the problem can be modeled by a right trianlge in which the side adjacent to the angle is 310 ft, and the side opposite the angle is the one we want to find. The relevant trig relation is ...

Tan = Opposite/Adjacent

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Solving for the Opposite side (the height of the balloon), we find ...

Opposite = Adjacent · Tan

height = (310 ft)·tan(22°) ≈ 125.25 ft

Enola's balloon is about 125.25 ft above the ground.

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Additional comment

If we assume Enola's angle measurement can have a possible error of ±0.5°, then the corresponding error in the balloon height is more than ±3 ft. It is a bit of nonsense to report the height to the nearest 0.12 inches, (0.01 ft).

User Neilkimmett
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2.8k points