A plane must travel S15E at 720km/h. If the wind Is from S35W at 130km/h, what heading and airspeed should the pilot set to reach the destination.

Question

I got 648km/h E8.89S

Answer 1

Why do you think this is calculus? Seems to me it is the law of cosines/sines and geometry.

Draw the figure on cartesian coordinates. The side R=720 and it is at a angle 15 deg S of E. Draw sideW at S of W by 35 deg, length 130. Both rays go away from the center.
So the last side is what the pilot should be aiming. Call it side H(eading).
First, use your 10th grade geometry to figure the angle between W and R. I think it might be 130 deg.

Law of Cosines:
H^2=W^2 + R^2 -2*W*H*cos130
figure H, the air speed.
Now the heading angle. Look at The angle WtoH (call it angle r)
H/sin130=720/sin(r)
figure angle (r).

Now the actual heading.
Angle r+180-35= heading angle measusred from N to E, my diagram indictes it is more than 90 deg, so your final angle the way you present it might be S of E. Study your diagram to confirm this.