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

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?

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)?

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

Thanks!

You're very welcome!

Your approach is correct, but there is a small mistake in your calculation. Let's go through the problem step by step to find the correct answer.

When the pilot is flying due west, the plane's velocity consists of two components: the velocity due to the wind and the velocity of the plane in still air.

Let's call the velocity due to the wind Vw and the velocity of the plane in still air Vp. The given values are:
Vw = 82.0 km/h (toward the south)
Vp = 380.0 km/h

To find the direction in which the pilot should head, we need to consider the vector sum of these two velocities. The direction will be the direction of this resulting velocity vector.

To find the magnitude of the resulting velocity, we can use the Pythagorean theorem:

Vresult^2 = Vw^2 + Vp^2
Vresult = sqrt(Vw^2 + Vp^2)

Substituting the given values:
Vresult = sqrt(82.0^2 + 380.0^2)
Vresult ≈ 389.1 km/h

Now, to find the direction, we can use trigonometry. We will use the angle θ, which represents the direction of the resulting velocity vector from the west.

sin(θ) = Vw / Vresult
sin(θ) = 82.0 / 389.1

Taking the arcsin (or sin^-1) of both sides:
θ = arcsin(82.0 / 389.1)

Evaluating this using a calculator:
θ ≈ 11.813 degrees

Therefore, the pilot should head approximately 11.813 degrees north of west.

So, it seems that you made a calculation error in finding the value of theta. Ensure that you entered the values correctly into your calculator and try again.