To find:
The vertical change in elevation from the point where the surveyor is standing to the point on the mountain is miles.
Solution:
The figure for the given question is as follows:
Let the vertical height be x miles.
In the above triangle, the value of the trigonometric function tangent of angle of elevation is:
[tex]\tan18=\frac{x}{4}[/tex]
Solve the above equation to find x:
[tex]\begin{gathered} 0.325=\frac{x}{4} \\ \Rightarrow x=1.299 \\ \Rightarrow x=1.3 \end{gathered}[/tex]
Thus, the answer is 1.3 miles.
