Question

From a hot-air balloon, Enola measures a 22° 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.

Answer 1

125.25 ft

Explanation:

You want the height of a balloon when the angle of depression is 22° to a landmark 310 feet away horizontally.

Tangent

The tangent function relates the sides of a right triangle to one of the acute angles.

Tan = Opposite/Adjacent

Application

In this scenario, this becomes ...

tan(22°) = (balloon height)/(310 ft)

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

The balloons vertical distance above the ground is about 125.25 feet.

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Additional comment

The attachment shows the angle as an angle of elevation. Since the horizontal reference at the balloon is parallel to the ground, the angles of depression and elevation are "alternate interior angles" with respect to the line of sight, so are congruent.

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