From her eye, which stands 1.66 meters above the ground, Deondra measures the angle of elevation to the top of a prominent skyscraper to be 70degrees
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. If she is standing at a horizontal distance of 276 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
Answer
To find the height of the skyscraper, we can use trigonometry.
Let h be the height of the skyscraper. We can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the skyscraper and the adjacent side is the horizontal distance between Deondra and the base of the skyscraper.
tan(70°) = h / 276
h = 276 * tan(70°)
h ≈ 776.6 meters
Therefore, the height of the skyscraper is approximately 776.6 meters.