Question

A surveyor measures the angle of elevation to a point on a mountain to be 18 degrees 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?

Answer 1

Answer:

1.3 miles

Step-by-step explanation:

Solution:-

- The surveyor stands at a platform that is B = 4 miles and at an elevation of θ = 18 ° away from the point on the mountain.

- We can construct a right triangle from surveyor to the point of observation. To determine the change in height/elevation (H) we will apply the trigonometric relation as follows:

                              tan ( θ ) = H / B

- Solve for the elevation (H):

                              H = B*tan ( θ )

                              H = 4*tan ( 18 )

                              H = 1.3 miles

- The change in elevation from surveyor to point of observation is H = 1.3 miles.

Answer 2

This is right triangle trig and you are looking for the height of the triangle. The reference angle is 18 degrees, the side adjacent to that angle is 4 and you are looking for the side opposite the reference angle.  The trig identity that helps us find that missing side is tangent:
$tan(18)= \frac{x}{4}$
and 4 tan(18) = x.
x = 1.3 miles