Velocity as a Vector: Plane Ground Velocity Calculation

[Random-Hero-]

Homework Statement

A light plane is traveling at 175km/h on a heading of N8°E in a 40km/h wind from N80°E. Determine the plane's ground velocity.

Homework Equations

The Attempt at a Solution

After I did all the graphing and trig. I came out with x^2 = 175^2 + 40^2 - 2(175)(40)cos108

which ends up being roughly 191.18, but the answer tells me its 167 km/h, N5°W

If anyone could help me out with this it would really be great, I am having a rough time with it.

Thanks for your time.

 

[phreak]

Break it up into components: NS, EW. The direction NS is y = 175 sin(82) - 40 sin(10), where + is N. The direction EW is x = 175cos(82)-40cos(10), where + is E. To get their length, calculate D = \sqrt{x^2+y^2}. I'll leave the direction to you.

 

[Random-Hero-]

Thanks a bunch! that helped tons!