Question

An airplane is flying in the direction 148° with an airspeed of u = 865 kilometers per hour. Because of the wind, its groundspeed and direction are v = 780 kilometers per hour and 140°, respectively (see figure in the link below). Find the direction and speed of the wind. (Round your answers to one decimal place.)
www.webassign.net/larpcalclim2/6-3-101-alt.gif

speed: (in km/h)
direction: N ? ° E

but the answer i got was:
speed: 142.68
direction: N 1.25 ° E
but i got the direction wrong and the speed correct?

Answer 1

I did it using vectors, and then again using the cosine law, and got the same 142.68 as you did

according to the wording as well as your diagram,
let the wind vector be v
v^2 = 865^ + 780^2 - 2(865)(780)cos8°
v = 142.679 , you had that.
then by the sine law in your diagram
sinø/780 = sin8/142.679
ø = 49.5° , with a bit of geometry using supplementary angles and parallel lines
the direction of the wind is 49.5 - 40 or 9.5°

Using vectors
vector v = 865(cos148,sin148) - 780(cos140,sin140)
= (-733.5616, 458.38) - (-597.515, 501.3743)
= (-136.047, -42.994)
|v| = √((-136.047)^2 + (-42.994)^2) = appr142.679 , same as before
tan(direction angle) = -42.994/-136.047 = .316..
direction angle = 17.54°

(perhaps you can check my arithmetic to see why they are not the same,
I can't locate my error at this point)

Answer 2

thanks Reiny, your answers is correct because i submitted 142.68 and 17.54 and it is correct