Honors Trig.
posted by Ashley on .
A plane is flying at a speed and direction of 550 mph, 25 degrees north of west. There is a wind of 28 mph, at an angle of 19 degrees south of the east direction. How fast is the plane actually flying? What direction is the plane traveling?

Here is an easy way to do these.
1) convert all angles to 000N,090E, 180S, 270W
Example: 456@29deg S of E.
= 456@119
then convert to N, E coordinates.
V= 456(Cos119 N + Sin119 E)
Now for your problem:
V= 550(cos295 N +sin295 E)+28(cos109 N+ sin109)
combine N, E vector components:
V= N(550cos295+28cos109)+E(550sin295+28sin109)
do that math and you will have something like this
V= nnnn N + eeeee E
magnitude V= sqrt(nnnn^2+eeee^2)
direction= arctan (eeee/nnnn)
on the angle, be careful, as tangent is a repeating angle, it repeats each 180. So you may have to figure which quadrant.