Airplane Trig Problem

Question

An airplane with a top speed of 350 mph needs to maintain a course due east. However, it is a particularly windy day, and the wind speed is 65 mph blowing 43 degrees north of east. In what direction must the plane navigate to maintain its desired course?

Answer 1

I'm using a trig formula for an oblique triangle; to get angle α.

a^2+b^2-2ab(cosγ)=c^2

sides: a=65

b=350

c=?

angles: α=?

β=?

γ=137° (90+43)

65^2+350^2-(2*65*350)cos137°=c^2

4225+122,500-(45,500)*(-.7314)=c^2

126,7255-(-332765.9)=c^2

160,001^.5=400.001.....=c

We want >a.

So: a/sinα=b/sinβ=c/sinγ

65/sinα= 400/sin137°=586.51...

65/586.51=110.825.....asin=6.362.....°