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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 ab

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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

#1
+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
+20679
+10

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