Question

The angle of elevation from ground level to the top of a building is 62

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. If the observer is standing 300 feet from the building, how tall is the building? A) 265 B) 564 C) 141 D) 282

Answer 1

564

Step-by-step explanation:

To determine the height of the building, we can use the trigonometric relationship of tangent. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the height of the building, and the adjacent side is the distance from the observer to the building.

Given that the angle of elevation is 62 degrees and the observer is standing 300 feet from the building, we can set up the equation as follows:

tan(62°) = height / 300

To solve for the height, we can rearrange the equation:

height = tan(62°) * 300

Using a calculator, we can find that tan(62°) is approximately 1.8807.

Substituting this value into the equation, we get:

height = 1.8807 * 300

Calculating this expression, we find that the height of the building is approximately 564 feet.

Therefore, the correct answer is B) 564.