A DC9 aircraft leaves an airport from a runway whose bearing

A DC-9 aircraft leaves an airport from a runway whose bearing is N53°E. After flying for 3/4 mile, the pilot requests permission to turn 90° and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the aircraft? please show steps

Thank you!!!!

Solution

Solution:

Tangent of angle between runway and plane is 1/(3/4) = 4/3

arctan (4/3) = 53.12 degress

Adding this to the runway bearing give 106.12 degrees away from north

Subtracting this from 180 gives

=> 180 -106.12 = 73.88 degrees east of south

or south 73.88 deg east