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Aā€‹ DC-9 aircraft leaves an airport from a runway whose bearing is N4343degreesĀ°E. After flying for one half 1 2 ā€‹mile, the pilot requests permission to turn 90degreesĀ° and head toward the southeast. The permission is granted. After the airplane goes 1 mile in thisā€‹ direction, what bearing should the control tower use to locate theā€‹ aircraft? What is the bearing that the control tower should use to locate theā€‹ aircraft? ā–¼ S N nothingdegreesĀ° ā–¼ E W ā€‹(Round to the nearest tenth asā€‹ needed.)

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oladayoademosu

Answer:

103.4Ā° or S76.6Ā°E

Explanation:

The direction N43Ā°E is perpendicular to the direction south-east when the plane turn 90Ā° and heads in the south-east direction.

Since the distance 1/2 mile N43Ā°E is perpendicular to the distance 1 mile south-east, we have a right angled triangle.

So, the angle Īø between the aircraft's new position and old position is gotten from tanĪø = 1 Ć· 1/2 = 2

Īø = tanā»Ā¹(2) = 63.43Ā°

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

Since we need the south-east bearing, the angle from south is 180Ā° - 103.43Ā° = 76.57Ā° ā‰… 76.6Ā°

So, our bearing is 103.4Ā° or S76.6Ā°E

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