Question

A surveyor measures of angle of elevation to a point on a mountain to be 18° the point of 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 how many miles

Answer 1

1.30 miles

Explanation:

The tangent relation is ...

tan(angle) = opposite/adjacent

The height of the surveyed point is the side of the right triangle that is opposite the angle of elevation. The horizontal distance to the surveyed point is the side of the triangle adjacent to the angle of elevation. So, we have ...

tan(18°) = height/(4 mi)

height = (4 mi)tan(18°) = 1.300 mi

The vertical change in elevation from the surveyor to the surveyed point is 1.300 miles.