Question

From her eye, which stands 1.68 meters above the ground, Hannah measures the angle of elevation to the top of a prominent skyscraper to be 31degrees

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. If she is standing at a horizontal distance of 194 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.

Answer 1

To find the height of the skyscraper, we can use trigonometry. By using the tangent function and solving for the height, we find that the height of the skyscraper is approximately 159.99 meters.

Step-by-step explanation:

To find the height of the skyscraper, we can use trigonometry. Let's use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle. In this case, the opposite side is the height of the skyscraper, the adjacent side is the horizontal distance from Hannah to the base of the skyscraper, and the angle of elevation is 31 degrees.

First, we need to convert the angle from degrees to radians, since the tangent function requires radians. We can use the formula: radians = degrees × π / 180. So, 31 degrees ≈ 0.54 radians.

Next, we can use the tangent function: tan(0.54 radians) = opposite / adjacent. Plugging in the values we know, we get: tan(0.54) = height / 194. Rearranging the formula, we can solve for the height: height = tan(0.54) × 194. Using a calculator, we find that the height of the skyscraper is approximately 159.99 meters.