Black diamond run

Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. To the nearest tenth, determine the angle of elevation to the top of the ski run.

Correct result:

A =  45.3 °

Solution:

$$\begin{gathered} a=8625\text{ ft } \\ b=3800\text{ ft } \\ x=4775\text{ ft } \\ y=a-b=8625-3800=4825\text{ ft } \\ \tan A={\displaystyle \frac{y}{x}} \\ {A}_1=\arctan ({\displaystyle \frac{y}{x}})=\arctan ({\displaystyle \frac{4825}{4775}})\doteq 0.7906\text{ rad } \\ A=A_1{\to }^{\circ }=A_1\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=0.7906\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=45.3^{\circ }=45^{\circ }17^{\mathrm{\prime }}54\mathrm{"} \end{gathered}$$

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