Question

From the observation deck of a skyscraper, Lavaughn measures a 42° angle of

depression to a ship in the harbor below. If the observation deck is 872 feet high,
what is the horizontal distance from the base of the skyscraper out to the ship?
Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

968.45 ft

Explanation:

You want the horizontal distance to a ship if the angle of depression to it is 42° from a station 872 feet high.

Tangent

The tangent relation is ...

Tan = Opposite/Adjacent

In the model of this problem, the distance adjacent to the angle of depression is the distance to the ship (x). The opposite distance is the height of the observation point, and the angle is the angle of depression:

tan(42°) = (872 ft)/x

x = (872 ft)/tan(42°) ≈ 968.45 ft

The horizontal distance to the ship is 968.45 feet.

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