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20 October, 18:49

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.)

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  1. 20 October, 19:27
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    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
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