Answer:
357 mph on a heading of 157°
Step-by-step explanation:
You want the resultant speed and direction of an airplane with a speed of 350 mph on a heading of 160° in a west wind at 20 mph.
Sum
The wind vector of 20 mph on a heading of 90° is added to the plane's vector of 350 mph at 160°. The resultant is found by a suitable calculator to be 357.33 mph on a heading of 156.99°.
The resultant speed is about 357 mph on a heading of 157°.
__
Additional comment
In the absence of a suitable calculator, you can use the law of cosines to find the resultant speed:
r = √(p² +w² -2pw·cos(110°))
r = √(350² +20² -2·350·20·(-0.34202)) ≈ √127688.2820
r ≈ 357.33 . . . . . . resultant speed
The effect on the plane's direction can be found from the law of sines.
α = arcsin(20/357.33·sin(110°)) ≈ 3.01°
So, the plane's resultant heading is ...
160° -3° = 157°. . . . . resultant direction.
