Solving trig problem for trajectory

[PhysicsAdvice]

Need to find the angle at which a plane should aim if when traveling at 210km/h with a 40km wind east produces a resultant angle of 60 degrees. I can write that 60=tan^-1(210sin60/(210cos60+40)

and proceed from there:

tan60=210sinx/(210cosx+40)
1.73=210sinx/210cosx+40
69.2+363cosx=210sinx
0.329+1.728cosx=sinx
0.329=sinx-1.728cosx

is there a trig law i can do to simplify? Thanks all, will keep at it!

 

[gneill]

You can use the sin² + cos² = 1 identity to replace sin or cos in your equation. Isolate the square root on one side and square both sides to eliminate it. You'll end up with a quadratic in either cos(x) or sin(x).