Question

Fill in the blank. A surveyor measures the angle of elevation to a point on a mountain to be 18 9. The point on the mountain is horizontally 4 miles away from the surveyor. The vertical change in elevation from the point where the surveyor is standing to the point on the mountain is miles. (Round your answer to the nearest hundredth of a mile.)

Answer 1

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:

`\tan18=(x)/(4)`

Solve the above equation to find x:

`\begin{gathered} 0.325=(x)/(4) \\ \Rightarrow x=1.299 \\ \Rightarrow x=1.3 \end{gathered}`

Thus, the answer is 1.3 miles.