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 36degrees ∘ . 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.
We can use trigonometry to solve this problem.
Let's consider the triangle formed by Sadie, the top of the skyscraper, and the base of the skyscraper. The angle of elevation is the angle between Sadie's line of sight and the horizontal line. The height of the skyscraper is the side opposite to this angle.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
In this case, the angle is 36 degrees, the adjacent side (horizontal distance) is 275 meters, and we want to find the opposite side (height of the skyscraper), so we can rearrange the formula and solve for the height:
opposite = tan(angle) * adjacent
opposite = tan(36°) * 275
opposite ≈ 0.7265 * 275
opposite ≈ 199.79 meters
So, the height of the skyscraper is approximately 199.79 meters. Rounded to the nearest hundredth, the height is 199.79 meters.