A surveyor determines that the angle of elevation to the top of a vertical building from a pt on level ground is 38deg. She then moves....

A surveyor determines that the angle of elevation to the top of a vertical building from a pt on level ground is 38deg.

She then moves back 50 feet & determines that the angle of elevation is 32 deg.

Find the height of the building.

$\begin{array}{|rcll|} \hline \dfrac{\sin(6^\circ)}{50} &=& \dfrac{\sin(32^\circ)}{y} \\ \mathbf{y} &=& \mathbf{ \dfrac{50\sin(32^\circ)}{\sin(6^\circ)} } \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline \sin(38^\circ) &=& \dfrac{h}{y} \\ h &=& y\sin(38^\circ) \\ h &=& \dfrac{50\sin(32^\circ)\sin(38^\circ)}{\sin(6^\circ)} \\ \mathbf{h} &=& \mathbf{ 156\ \text{feet} } \\ \hline \end{array}$