Question

From the observation deck of a skyscraper, Morgan measures a 67

∘ angle of depression to a ship in the harbor below. If the observation deck is 955 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

To find the horizontal distance from the base of the skyscraper out to the ship, use the tangent function with the angle of depression and height of the observation deck. Plug the values into the equation x = 955 / tan(67°) to find the horizontal distance, approximately 356.69 feet.

Step-by-step explanation:

To find the horizontal distance from the base of the skyscraper out to the ship, we can use trigonometry. Given that Morgan measures a 67° angle of depression and the observation deck is 955 feet high, we can use the tangent function to find the horizontal distance. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the observation deck and the adjacent side is the horizontal distance we want to find. So, tan(67°) = 955 / x, where x is the horizontal distance. Rearranging the equation to solve for x, we get x = 955 / tan(67°).