Hello, kmjt!

Your diagram is incorrect . . .

A plane is heading S 70° W with a groundspeed of 625 km/h.

If the pilot is steering west at an airspeed of 665 km/h,

. . what must be the windspeed and wind direction? Code:

665
A o - - - - - - - - - - - o O
\ 20° *
\ *
\ *
\ * 625
\ *
o
B

The plane is flying from O to A at 665 km/hr.

. . $\displaystyle \angle AOB = 20^o$

The wind is blowing from A to B.

The plane's resultant flight is: .$\displaystyle OB = 625$ km/hr.

Law of Cosines: . $\displaystyle AB^2 \:=\:665^2 + 625^2 - 2(665)(625)\cos20^o \;=\;51,\!730.50897$

. . Hence: .$\displaystyle AB \;\approx\;227.4$

Then: .$\displaystyle \cos A \;=\;\frac{665^2 + 227.4^2 - 625^2}{2(665)(227.4)} \;=\;0.341588668$

. . Hnce: .$\displaystyle \angle A \;\approx\;70^o$

Therefore, the windspeed is 227.4 km/hr and its direction is: .S 20° E.

Interesting!

Triangle ABO is virtually a right triangle . . .

.