An airplane is headed in direction 58 with an air speed of 150 mph. the course is 72 with a ground speed of 130 mph. find the direction of the wind.

The direction where it is headed is the ideal direction while the course is the actual. There is a difference due to the wind force. Since the course is greater than the ideal direction, then the wind must be moving the plane towards the y-axis direction.

If we draw the lines at the same origin, we see that the angle between the actual and ideal directions is:

72˚ - 58˚ = 14˚

Using cosine law to calculate for the speed of wind, c:

c^2 =  150^2 + 130^2 – 2(150)(130)cos14

c^2 = 1558.47

c = 39.48 mph

Using sine law to calculate for the angle θ:

39.48 / sin14 = 130 / sinθ

sinθ = 0.8

θ = 52.81˚

Now this is the angle inside the triangle. The direction of the wind is:

180 + 58˚ - 52.81˚ = 185.2˚

The direction of the wind is around 185.2˚.