Relative velocity - plane flying

[jensson]

Homework Statement

A plane flies at an airspeed of 250 km/h. A wind is blowing at 80 km/h toward the direction 60* east of north.
a) In what direction should the plane head in order to fly due north relative to the ground?
b) What is the speed of the plane relative to the ground?

Homework Equations

it's too messy to write the equations down, but I used position vector of plane relative to the ground and the Pythagorean theorem

The Attempt at a Solution

for a:

sin x = 30/250 = 8/25

sin inverse 8/25 = 19 degrees

so my answer to a is 19 degrees west of north. the back of the book says the answer is 16 degrees west of north. What did I do wrong?



for b:

V (plane to ground) = squar root of (250^2 + 80^2) = 237 km/h

the answer in the back of the book is 280 km/s so even even I converted to seconds my answer would be way off. Again, I don't know what I did wrong...

 

[jensson]

anyone?