Question

Finding the Height of a Mountain Use the illustration in Problem 39 to find the height QD of the mountain.

Short answer

The mountain is 629.9 feet tall.

Step-by-step solution

Step 1. Given Information

The distance from the bottom of the mountain P to the top Q is $PQ=1490.48feet$

A surveyor measures angle of elevation from the bottom P to the top of the mountain Q is$\angle DPQ={25}^{\circ }$

Step 2. Find the height of mountain by Sin Law

$$\begin{gathered} \frac{\sin {25}^{\circ }}{DQ}=\frac{\sin {90}^{\circ }}{1490.48} \\ DQ=\sin {25}^{\circ }\frac{1490.48}{\sin {90}^{\circ }} \\ DQ=629.9ft \end{gathered}$$