Question

The angle of elevation from a point on the ground to the top of a pyramid is 37 degrees 50​' The angle of elevation from a point 183 feet farther back to the top of the pyramid is 18 degrees 10​'. Find the height of the pyramid.

Answer 1

Answer:

The height of the pyramid is approximately 104 Ft. See the graphic attached.

Explanation:

First, you have to plot to realize that you have two rectangle triangles, formed by the different elevation points of view. From there you can have a system of two equations, with two unknown values.

Equation (1)

$tan 37^{o}50'= \frac{Ph}{x} \\\\Ph=tan 37^{o}50' x= 0.7766 x$

Equation (2)

$tan 18^{o}10'=\frac{Ph}{x+183} \\\\Ph=[tan 18^{o}10'][x+183]=[0.3281][x+183]$

Matching (1) and (2)

$0.7766 x=0.3281(x+183)\\\\(0.7766-0.3281)x=60.05\\\\x=\frac{60.05}{0.4485} =133.89ft$

replacing x value in (1)

$Ph=0.7766*133.89=103.9789\\Ph = 104 ft$