Question

The angle of elevation from a point on the ground to the top of a pyramid is 33°10'. The angle of elevation from a point 132 feet farther back to the top of the pyramid is 26°20'. Find the height of the pyramid.

A. 26
B. 132

Answer 1

To determine the height of the pyramid, the angles of elevation from two different points and their distance apart are used. By setting up a system of equations using the tangent function for each triangle formed by the lines of sight to the pyramid's top, one can solve for the pyramid's height.

Step-by-step explanation:

To find the height of the pyramid, we can use the concept of elevation angles and trigonometry. Consider two right triangles that share a common vertical side, which is the height of the pyramid we want to find. The first triangle includes the height of the pyramid and the initial observation distance from the pyramid, and the second triangle includes the height of the pyramid and the observation distance from the pyramid plus an additional 132 feet.

Let's denote the height of the pyramid as h. For the first triangle with the angle of elevation of 33°10', using the tangent function, we get:

• tan(33°10') = h / d

For the second triangle with the angle of elevation of 26°20' and the additional 132 feet distance, we get:

• tan(26°20') = h / (d + 132)

To solve for h and d, we set up a system of two equations:

1. h = d · tan(33°10')
2. h = (d + 132) · tan(26°20')

By equating the two expressions for h and solving for d, we can then find the height h. By performing the calculations with the specific tangent values, we can find the exact height of the pyramid.