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# 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....

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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!

Dec 11, 2019

#1
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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.

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

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

Dec 11, 2019
#2
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But of course! I had to subtract 38-32 to get 6. I see it now. Thank you so much! your answers are so easy to understand

Roxettna  Dec 11, 2019
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Thank you, Roxettna !

heureka  Dec 11, 2019