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**+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

#1**+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