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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

Best Answer 

 #1
avatar+20679 
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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
 #1
avatar+20679 
+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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