Chapter 12.5, Problem 5P

To determine

Find the vertical distance between the bottom of the ski lift and the summit.

Answer to Problem 5P

545 ft.

Explanation of Solution

Given:

The angle of elevation of the summit of a mountain from the bottom of a ski lift is $33°$ .A skier rides 1000 ft on this ski lift to get the summit.

Formula Used:

  $\sin \theta =\frac{\text{length of opposite side to }\theta }{\text{length of hypotenuse}}$

Calculation:

Represent the given situation :

  

We need to find y .

Use the sine formula :

  $\begin{array}{l}\sin 33°=\frac{\text{length of opposite side to 33}°}{\text{length of hypotenuse}}\\ \Rightarrow \sin 33°=\frac{y}{1000}\\ \Rightarrow y=1000\sin 33°\mathrm{...................}[\text{multiply each side by 1000]}\\ \Rightarrow y=545\end{array}$

So, the vertical distance between the bottom of the ski lift and the summit is 545 ft.