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Chapter 8: Q. 63 (page 517)

A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40°E. After flying for 12mile, 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?

Short Answer

Expert verified

The bearing of the plane from East is103.63°

Step by step solution

01

Given Information

Given that a DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40°E. After flying for 12mile, 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.

02

Solution

The distance of 12mile 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 East by an angle of 40°.

Now, we can draw a figure as: -

We have to find angle x.

In, △ABC

tan(x°)=ABBCtan(x°)=10.5tan(x°)=2x°=tan-1(2)x°=63.4349°

Taking the bearing of the runway into consideration, the bearing of the plane from East is40°+63.43°=103.43°

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