From the observation deck of a skyscraper, Bentley measures a 48degrees ∘ 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.
Question
From the observation deck of a skyscraper, Bentley measures a 48degrees ∘ 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.
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (height of the skyscraper) to the adjacent side (horizontal distance we want to find).
The formula for tangent is tan(θ) = opposite/adjacent.
Here, the angle θ is 48 degrees and the opposite side is 969 feet. We want to find the adjacent side (let's call it x).
So, we have:
tan(48) = 969/x
To solve for x, we rearrange the equation to get:
x = 969/tan(48)
Now, we just need to calculate the value of 969 divided by the tangent of 48 degrees.
After calculating, we get x ≈ 969/1.11061 ≈ 872.3 feet.
So, the horizontal distance from the base of the skyscraper out to the ship is approximately 872.3 feet.
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