How to determine the actual velocity of a plane with one known angle?

An airplane flying at 500 km/h NW encounters a wind of 120 km/h blowing in the direction W25degrees South. Determine the actual velocity of the plane.How to determine the actual velocity of a plane with one known angle?Imagine that you start at point A, then travel 500km northwest (I assume that's north 45 degrees west) to point B, then travel 120km west 25 degrees south to point C. So now points A, B, and C form a triangle.

Angle B = 45 + 90 - 25 = 110 degrees

To find the length of b (AC), use the Law of Cosines:
b^2 = a^2 + c^2 - 2ac*cos(B)
b^2 = 120^2 + 500^2 - 2*120*500*cos(110)
b^2 = 14400 + 250000 - 120000*cos (110)
b = sqrt(264400 - 120000*cos (110))
b =~ 552.668 km/h

To find angle A, use the Law of Sines:
sin(A) / a = sin(B) / b
sin(A) = (a/b) * sin(B)
A = arcsin((a/b) * sin(B))
A =~ arcsin((120/552.668) * sin(110))
A =~ arcsin((120/552.668) * sin(110))
A =~ 11.772951906935072809780400289736