Asurveyor measures the angle of elevation to a point on a mountain to be 12 degrees. the point on the mountain is horizontally 5 miles away from the surveyor. what is the vertical change in elevation from the point where the surveyor is standing to the point on the mountain? (round your answer to the nearest hundredth of a mile.)

From the right triangle formed, the adjacent side to the angle of elevation is 5 miles and the vertical change in elevation is the opposite side. From the trigonometric function, tangent of an angle,
                             tan 12° = x / 5 miles
The value of x from the equation is 1.06 miles. Thus, the vertical change in elevation is 1.06 miles.