To find the vertical change in elevation, we can use the tangent function, which relates the angle of elevation to the vertical and horizontal distances.
In this case, the horizontal distance is given as 5 miles, and the angle of elevation is 12 degrees. Let's denote the vertical change in elevation as "x" miles.
Using the tangent function:
tan(12°) = x/5
To solve for x, we can multiply both sides by 5:
5 * tan(12°) = x
Using a calculator, we can evaluate the value of tan(12°) to be approximately 0.21256.
Therefore, the vertical change in elevation from the point where the surveyor is standing to the point on the mountain is approximately:
x ≈ 5 * 0.21256 ≈ 1.0628 miles
Rounded to the nearest hundredth of a mile, the vertical change in elevation is approximately 1.06 miles.
