Question

9. A small airplane is 60 miles from the airport and is going down for landing with some angle of depression. However its navigation device malfunctions and incorrectly shows the distance to be 65 miles. The dispatcher noticed this mistake and figured out that if airplane continues on its current course, it will end up 16 miles from airport. By how many degrees should dispatcher adjust the airplane heading

Answer 1

13.98 degrees

Explanation:

Let the airplane be at point A, the airport at point B and the point of overshoot, point C.

If the plane is on path AC and the pilot wants to adjust to the path AB, the angle by which the pilot will adjust the airplane heading is the angle between AB and AC which is A.

Using Cosine Rule

`Cos A=(b^2+c^2-a^2)/(2bc) \\Cos A=(65^2+60^2-16^2)/(2(65)(60)) \\Cos A=0.9704\\A=arcCos (0.9704)\\\angle A=13.98^\circ`

The pilot should adjust the plane's heading by 13.98 degrees.