Helicopter Speed Relative to Ground: Solve w/ Vector Components

[Delber]

Homework Statement

A helicopter's velocity relative to the air is 55m/s[W35$$^\circ$$N]
The wind speed is 21 m/s[E].
I need to find the speed of the airplane relative to the ground.

Homework Equations

The Attempt at a Solution

I tried using vector components for this equation. Since the vertical component of the vector of the helicopters speed relative to the air is the same as the vector of the helicopters speed relative to the ground and the horizontal component should be the horizontal component of the helicopter's velocity relative to the air minus the wind speed.
I tried it this way and the answer is different from the one given by the textbook. I'm not very confident with vector components.

Edit: I did it using the cosine law and got the correct answer, but I would like to know if there was any faults with the way I tried to do it with vector components.

 

[jk4]

There doesn't appear to be any faults with your description of using vectors. Perhaps you just made an error.