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Stephan is standing on a mesa at the Painted Desert. The elevation of the mesa is about 1380 meters and Stephan's eye level is 1.8 meters above ground. If Stephan can see a band of multicolored shale at the bottom and the angle of depression is 29 degrees, about how far is the band of shale from his eyes?

Guest Jul 14, 2015

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 #1
avatar+18715 
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Stephan is standing on a mesa at the Painted Desert. The elevation of the mesa is about 1380 meters and Stephan's eye level is 1.8 meters above ground. If Stephan can see a band of multicolored shale at the bottom and the angle of depression is 29 degrees, about how far is the band of shale from his eyes?

 

$$\small{\text{$
\begin{array}{rcl}
\sin{(29\ensurement{^{\circ}})} &=& \dfrac{1380~\mathrm{m}+1.8~\mathrm{m}}{s}\\\\
s &=& \dfrac{1380~\mathrm{m}+1.8~\mathrm{m}}{ \sin{(29\ensurement{^{\circ}})} }\\\\
s &=& \dfrac{ 1381.8~\mathrm{m} }{ 0.48480962025 }\\\\
\mathbf{s} & \mathbf{=} & \mathbf{2850.19 ~\mathrm{m}}
\end{array}
$}}$$

 

 

The band of shale is 2850.19 m far from his eyes.

 

heureka  Jul 15, 2015
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1+0 Answers

 #1
avatar+18715 
+10
Best Answer

Stephan is standing on a mesa at the Painted Desert. The elevation of the mesa is about 1380 meters and Stephan's eye level is 1.8 meters above ground. If Stephan can see a band of multicolored shale at the bottom and the angle of depression is 29 degrees, about how far is the band of shale from his eyes?

 

$$\small{\text{$
\begin{array}{rcl}
\sin{(29\ensurement{^{\circ}})} &=& \dfrac{1380~\mathrm{m}+1.8~\mathrm{m}}{s}\\\\
s &=& \dfrac{1380~\mathrm{m}+1.8~\mathrm{m}}{ \sin{(29\ensurement{^{\circ}})} }\\\\
s &=& \dfrac{ 1381.8~\mathrm{m} }{ 0.48480962025 }\\\\
\mathbf{s} & \mathbf{=} & \mathbf{2850.19 ~\mathrm{m}}
\end{array}
$}}$$

 

 

The band of shale is 2850.19 m far from his eyes.

 

heureka  Jul 15, 2015

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