Question

Find the length of the base of the following pyramid, given the height of the pyramid is 91 meters and the angle of elevation of the base of the pyramid is 52°. Round to the nearest whole number.

An image of a square pyramid is shown with a right triangle embedded inside it. The face is at an incline of 52 degrees. The height is labeled 91, and the corner of the right angle is marked with a letter P.

142 meters
197 meters
231 meters
295 meters

Answer 1

Explanation:

To find the length of the base of the pyramid, we can use trigonometry and the given information.

In the given image, the height of the pyramid is 91 meters, and the angle of elevation of the base is 52 degrees. We can label the length of the base as "b."

Using trigonometry, we know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pyramid (91 meters), and the adjacent side is the length of the base (b).

Therefore, we can write the equation:

tan(52°) = 91 / b

To find the length of the base, we can rearrange the equation:

b = 91 / tan(52°)

Calculating this using a calculator:

b ≈ 142 meters

Rounding to the nearest whole number, the length of the base of the pyramid is 142 meters.