Solution:
Given:
The sketch shows the description of the surveyor
The angle of elevation is given in degrees, minutes, and seconds.
Converting this to degrees only,

Representing the sketch as a line diagram,
This line diagram can further be represented by two right triangles;
Using the trigonometric identity of tangent to get the height (h) in both right triangles;

Hence, from triangle A,

Also, from triangle B,

Hence, equating the height (h) gotten in both triangles,

To get the height of the mountain; recall from triangle B,

Therefore, the height of the mountain to the nearest whole foot is 3661 foot