Question

The nose of a plane is pointing west with an airspeed of 350 km/h. The plane’s resultant ground velocity is 315 km/h [S75°W]. Determine the speed and direction of the wind, correct to 2 d.p. Include a labeled diagram with your solution.

I got 81.53 km/h [S] but I think I may be wrong

Answer 1

For wind velocity I will use the direction the wing is GOING
( In other words a North wind goes South)
Wind velocity East = Ve
Wind velocity South = Vs
Total velocity west = 350 - Ve = 315 sin 75
Total velocity south = Vs = 315 cos 75

Answer 2

According to my sketch, if the speed of the wind is x km/h
by the cosine law:
x^2 = 350^2 + 315^2 - 2(350)(315)cos15°
x = appr 93.479 km/h

then by the sine law, if the angle opposite the side 315 is A
sinA/315 = sin15/93.479
I get A = 60.71°
so the wind has a speed of 93.48 km/h in the direction of S 29.29° E

check my arithmetic, I did not write any of this down first.