Direction problem; find angle to shortest path with wind

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caveman127
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Homework Statement


A pilot must travel directly to a town 500 miles away in a directions 20 degrees east of south from her present position. There is a steady 40 mph wind blowing west to east. Her plane's cruising speed through calm air is 95 mph. Using vector, what must be the plane's heading.

Homework Equations


tan-1(Ay/Ax) = angle of vector A.

The Attempt at a Solution


Vp/e = 95 mph south
Va/e = 40 mph east
Add vectors to get Vp/a = -95i + 40j → |Vp/a| = 103.078 mph
Angle of Vp/a = tan-1(-95/40) = -67.2 degrees from...east? so 67.2 south of east.

I feel like this is pretty far off, because I do anything with the fact the town is 500 miles away and 20 degrees east from south. Please help if you can :)
 
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You might start by drawing a somewhat scaled vector diagram of this situation and you will see that 67.2 S of East is wrong. Also, I think that 103.078 is incorrect also. Once you get a good diagam, this is a trig problem.