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.

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)

[tex]tan 37^{o}50'= \frac{Ph}{x} \\\\Ph=tan 37^{o}50' x= 0.7766 x[/tex]

Equation (2)

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

Matching (1) and (2)

[tex]0.7766 x=0.3281(x+183)\\\\(0.7766-0.3281)x=60.05\\\\x=\frac{60.05}{0.4485} =133.89ft[/tex]

replacing x value in (1)

[tex]Ph=0.7766*133.89=103.9789\\Ph = 104 ft[/tex]

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.

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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.