An airplane is headed on a bearing of 130 degrees at an airspeed of 261 km per hr. A 58 km per hr wind is blowing from a direction of 217 degrees. Find the groundspeed and resulting bearing of the plane.
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From the diagram attached
Angle ABC = 217 – 130 = 87
Using the cosine rule
b² = a²+ c² – 2ac Cos B
b² = 58² + 261² – 2x58x261 Cos 87
= 69900.4766
b = 264.4 km/h
Getting angle BAC using Sine rule
a/Sin A = b/Sin B
58/Sin A = 264.4/ Sin 87
Sin A = (58XSin87)/264.4 = 0.219
A = 12.7
Bearing angle = 130 – 12.7 = 117.3
Ground speed = 264.4 km/h
Bearing = 117.3
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