An airplane is flying at an altitude of 6 miles (approximately 32,000 feet) toward a point directly above where you are standing. If you are standing x miles away from a spot that is perpendicular to the plane, what is the equation that relates the angle as a function of x? Then, using that equation, solve for when x is 2 miles.

angle = arc tangent(6/x)

for x=2 -> angle = 71.565°

Step-by-step explanation:

To find the relation of the distance x and the angle of elevation that you are seeing the airplane, we should use the tangent relation of the angle. The opposite side of the angle is the altitude of the airplane, and the adjacent side of the angle is the distance x.

So we have that:

tangent(angle) = 6/x

angle = arc tangent(6/x)

If we have the value of x = 2, the angle will be:

angle = arc tangent(6/2) = arc tangent(3)

angle = 71.565°