Question

Find the length of the base of the following pyramid, given the height of the pyramid is 221 meters and the angle of elevation of the base of the pyramid is 62°. 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 62 degrees. The height is labeled 211, and the corner of the right angle is marked with a letter P.

104 meters
118 meters
235 meters
416 meters

Answer 1

The length of the base of the pyramid is approximately 416 meters.

To find the length of the base of the pyramid, we can use trigonometry. Let's call the length of the base "x". We know that the height of the pyramid is 221 meters and the angle of elevation of the base is 62 degrees. The angle of depression from the top of the pyramid to the base is also 62 degrees.

Using trigonometry, we can set up the following equation:

tan(62) = 221/x

To solve for x, we can multiply both sides by x and divide both sides by tan(62):

x = 221/tan(62)

Using a calculator, we can evaluate this expression to get:

x ≈ 416 meters

Therefore, the length of the base of the pyramid is approximately 416 meters.