xibaryon wrote:

An airplane whose air speed is 620 km/h is supposed to fly in a straight path 35.0 degree north of east. But a steady 95 km/h wind is blowing from the north. In what direction should the plane head?

Here is what I thought:

direction of the plane

after rearranging:

then how do you solve for theta?

is there a better way to do it?

Here's how to solve your equation. But it does suggest there may be a better way to set up the problem to make it easier to solve.

Write your equation as

then

Let

and

Use the second of these trig identities

to get

and

If anyone knows of a good web page describing this method, please let me know. The method is called introducing an auxiliary angle.