The question is the following:
An Airbus 4350 flies 900km/h in windless weather. In which compass direction does the Airbus need to head so that it goes straight to Southwest when the wind is 40m/s to east? In addition, what will be its speed?
I drew a picture with vectors and tried to solve the speed using law of cosines. I got a speed of 1007km/h which is obviously incorrect. What am I doing incorrectly and how should this be solved? Thanks a lot in advance.
hint...Your velocity triangle may be wrong. Convert the windspeed to 144 km/h.
The velocity triangle should have the unknown $v$ which is the speed of the plane relative to the ground pointing towards the South West. The velocity of the plane relative to the air is $900$ and points in a direction of $225+\alpha$. The third side of the triangle goes from West to East and has a magnitude of $144$.
Using the Sine Rule, you should get $\alpha=6.496^o$ and use the Sine Rule again to get $v=792.4$