From the observation deck of a skyscraper, Shaniece measures a 48degrees
∘
angle of depression to a ship in the harbor below. If the observation deck is 1121 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 trigonometry. The angle of depression forms a right triangle with the height of the observation deck (1121 feet) as one leg, the distance from the base of the skyscraper to the ship as the hypotenuse, and the vertical distance from the ship to the base of the skyscraper as the other leg.
We can use the tangent function to find the horizontal distance x:
tan(48°) = 1121 / x
x = 1121 / tan(48°)
x ≈ 1121 / 1.1106
x ≈ 1009.66 feet
Therefore, the horizontal distance from the base of the skyscraper out to the ship is approximately 1009.66 feet.