Physics plane/wind speed problem

[lmf22]

A plane is headed due south with a speed relative to still aire of 280km/h. After 1 hour the plane covered only 180km and their direction is not south but southeast. What is the wind velocity?

Any help would be great. Thank you.

 

[iamhumble]

This is how I am approaching the problem but I am unsure if I am right.

1) I drew a simple diagram to illustrate the problem (see attachement).
2) Side A is 280
Side B is 180
Side C is 215.5

So, I would think the wind velocity is 215 km.

 

[Ba]

That is not really right because in an hour the plane has traveled only 127 km due south ((180 km)cos 45 degrees east of south) because it is flying into a diagonal headwind. It has also traveled east ((180 km) sin 45 degrees east of south). These are the same so the east component of the wind vector is the ((180 km) sin 45 degrees east of south) while the north component is 280km-(180 km)sin 45 degrees. To get the magnitude of the wind vector you square the north component of the wind add the east component of the wind squared and take the square root. Use the positive number, magnitude is always positive.
(N^2+E^2)^.5= magnitude of the wind vector
The direction is then the inverse tangent of the (east component divided by the north component) east of north.
atan (E/N), degrees east of north