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From her eye, which stands 1.69 meters above the ground, Sadie measures the angle of elevation to the top of a prominent skyscraper to be 36 ∘ ∘ . If she is standing at a horizontal distance of 275 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

2 Answers

5 votes

We can use the tangent function to solve this problem. Let h be the height of the skyscraper.

First, we need to find the length of the adjacent side of the right triangle formed by Sadie, the base of the skyscraper, and the point where she is standing. This length is the horizontal distance between Sadie and the base of the skyscraper, which is 275 meters.

Next, we can use the tangent of the angle of elevation to find the ratio of the opposite side (the height of the skyscraper) to the adjacent side:

tan(36°) = h/275

Solving for h, we get:

h = 275 tan(36°)

Using a calculator, we find:

h ≈ 198.64 meters

Therefore, the height of the skyscraper is approximately 198.64 meters.

User Rdb
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7.9k points
7 votes

Answer: 201.49

Explanation:

User Anna Tolochko
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7.7k points