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.

It'd be greatly appreciated if steps would be shown of how to solve it!

Roxettna Dec 11, 2019

#1**+3 **

**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.**

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

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

heureka Dec 11, 2019