Question

From the observation deck of a skyscraper, Bentley measures a 48degrees

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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

To calculate the horizontal distance from the skyscraper's base to the ship, apply the tangent function from trigonometry, use the angle of depression and height of the observation deck to find the horizontal distance, and then round off to the nearest tenth.

Step-by-step explanation:

The student is asking how to calculate the horizontal distance from the base of a skyscraper to a ship if the angle of depression from the observation deck to the ship is 48 degrees and the height of the observation deck is 969 feet.

To find the horizontal distance, we'll use trigonometry. Specifically, we will use the tangent function because we have an angle and the opposite side (height of the skyscraper), and we want to find the adjacent side (horizontal distance to the ship).

Using the formula tangent of the angle equals opposite over adjacent (tan(θ) = opposite/adjacent), we rearrange to find the adjacent:

1. tan(48°) = 969/horizontal distance.
2. horizontal distance = 969 / tan(48°).
3. Calculate the tangent of 48° and then divide 969 by this value to find the horizontal distance.

Rounding off the answer to the nearest tenth gives the required horizontal distance.