## Trigonometry (11th Edition) Clone

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