Question

From the observation deck of a skyscraper, Bentley measures a 48 angle of depression to a ship in the harbor below. If the observation deck is 969 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary

Answer 1

So the horizontal distance from the base of the skyscraper out to the ship is approximately 872.4 feet.

Explanation:

We are given that the angle of depression is 48 degrees and that the height of the observation deck is 969 feet. Let's call the distance from the base of the skyscraper out to the ship "d".

We can use the tangent function to relate the angle of depression to the horizontal distance:
tan(48) = x / d

Multiplying both sides by d, we get:

d * tan(48) = x

Now we just need to plug in the values we know:
d * tan(48) = x

d * 1.1106 = x

Rounding to the nearest tenth, we get:
d = x / tan(48) ≈ 872.4 feet