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From the observation deck of a skyscraper, Lavaughn measures a 42degrees
∘
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.

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sqdancefan

Answer:

  968.45 ft

Step-by-step explanation:

You want the horizontal distance from an observer 872 feet high to a ship at an angle of depression of 42°.

Tangent

The tangent relation is ...

  Tan = Opposite/Adjacent

In this geometry, the vertical height of the building is opposite the angle of depression. The side adjacent to the angle is the distance to the ship. This means ...

  tan(42°) = (872 ft)/d

  d = (872 ft)/tan(42°) ≈ 968.45 ft

The distance out to the ship is about 968.45 ft.

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