Question

A DC-9 aircraft leaves an airport from a runway whose bearing is N54°E After flying for 3/4 mile, the pilot requests permission to turn 90 deg and head toward the southeast The permession 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?

Answer 1

The bearing of the plane is
095
°
or
S
85
°
E

Step-by-step explanation:
The distance of
3
4
mile after take-off, the
1
mile flown by the plane and the direct line from the control tower to the DC-9 form a right-angled triangle. It is offset from North by an angle of
42
°

Use trigonometry to find the angle at the control tower.
Opposite side =
1
mile and adjacent side is
3
4
mile
tan
θ
=
1
3
4
=
4
3

θ
=
53.1
°

Taking the bearing of the runway into consideration, the bearing of the plane from North is
42
°
+
53.1
°
=
095.1
°

Bearings are usually given with
3
figures, so
095
°

The other format would be in relation to the N-S line.
The place is on a bearing of
S
85
°
E