Question

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.

Answer 1

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