Answer
The height of the pyramid is 114 feet
Work Step by Step
Let $x$ be the distance from the vertical line to the first point.
We can write an expression for the height $h$:
$\frac{h}{x} = tan~35.5^{\circ}$
$h = x~tan~35.5^{\circ}$
We can use the second point to write another equation for the height $h$:
$\frac{h}{x+135} = tan~21.167^{\circ}$
$h = (x+135)~tan~21.167^{\circ}$
We can equate the two expressions to find $x$:
$x~tan~35.5^{\circ} = (x+135)~(tan~21.167^{\circ})$
$0.713~x = 0.387~x+52.27$
$0.713~x - 0.387~x = 52.27$
$x = \frac{52.27}{0.326}$
$x = 160~ft$
We can use the first equation to find $h$:
$h = x~tan~35.5^{\circ}$
$h = (160~ft)~tan~35.5^{\circ}$
$h = 114~ft$
The height of the pyramid is 114 feet
