Question

From a hot-air balloon, Addison measures a 27° angle of depression to a landmark

that's 989 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

503.9 ft

Explanation:

The geometry of the problem can be represented by a right triangle with one known leg, one unknown leg, and an acute angle adjacent to the known leg. The trigonometric function tangent is used to relate these measures:

Tan = Opposite/Adjacent

tan(27°) = height/(989 ft)

Multiplying by the denominator, we find ...

height = (989 ft)tan(27°)

height ≈ 503.9 ft

The balloon's vertical distance from the ground is about 503.9 feet.