From the observation deck of a skyscraper, Ian measures a 48degrees∘ angle of depression to a ship in the harbor below. If the observation deck is 871 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.
To solve this problem, we can use the tangent function, which relates the angle of depression to the ratio of the opposite side (height) to the adjacent side (horizontal distance).
Let's denote the horizontal distance from the base of the skyscraper to the ship as x. Then, using the tangent function:
tan(48°) = height/ x
Rearranging the equation, we get:
x = height / tan(48°)
Plugging in the values, we have:
x = 871 feet / tan(48°)
Using a calculator, we find:
x ≈ 871 feet / 1.1106
x ≈ 783.75 feet
Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 783.75 feet.