A DC-9 aircraft leaves an airport from a runway whose bearing is N4343degrees°E. After flying for one half 1 2 mile, the pilot requests permission to turn 90degrees° 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? What is the bearing that the control tower should use to locate the aircraft? ▼ S N nothingdegrees° ▼ E W (Round to the nearest tenth as needed.)

103.4° or S76.6°E

Explanation:

The direction N43°E is perpendicular to the direction south-east when the plane turn 90° and heads in the south-east direction.

Since the distance 1/2 mile N43°E is perpendicular to the distance 1 mile south-east, we have a right angled triangle.

So, the angle θ between the aircraft's new position and old position is gotten from tanθ = 1 ÷ 1/2 = 2

θ = tan⁻¹(2) = 63.43°

So, the total angle from North to its new position is 40° + 63.43° = 103.43°

Since we need the south-east bearing, the angle from south is 180° - 103.43° = 76.57° ≅ 76.6°

So, our bearing is 103.4° or S76.6°E