An airplane pilot wishes to fly due west. A wind of 82.0 km/h is blowing toward the south.

Question

If the airspeed of the plane (its speed in still air) is 380.0 km/h, in which direction should the pilot head?

This is what I did. I let
theta = arcsin(82.0/380.0)
theta = 12 degrees North of West

but I got it wrong I guess...Did I miss something?

Answer 1

The logic sounds good to me.
The southward component is 82 km/hr which is cancelled by 380 sin(θ).
The θ that I calculated is 12.462 degrees approx. north of west.
Is your answer from the computer requiring a definite number of decimal places, or is it on paper? Or perhaps the answer is expressed bearing, or 282.462 degrees (clockwise from the north)?

Answer 2

Ah, that was the problem. I only put 12 degrees, not 12.462.
Thanks!

Answer 3

You're very welcome!