Find unknown wind velocity given airlplane's speed

[Gardunf070]

Homework Statement

An aeroplane flies with an airspeed of 50.0 m/s [E40°N]. If the velocity of the plane, according to an observer on the ground, is 30.0 m/s [S45°E], what is the wind velocity?

Relevant Equations

Here is the answer:
The wind velocity is 56 m/s [W72°S]

But I don't understand how is that it ends up on the west side if both vectors were pointing east.

 

[BvU]

So what is  your answer for the wind speed?

 

[haruspex]

Homework Statement: An aeroplane flies with an airspeed of 50.0 m/s [E40°N]. If the velocity of the plane, according to an observer on the ground, is 30.0 m/s [S45°E], what is the wind velocity?
Relevant Equations: Here is the answer:
The wind velocity is 56 m/s [W72°S]

But I don't understand how is that it ends up on the west side if both vectors were pointing east.

Which two vectors add to make the third?

 

[Lnewqban]

Here is the answer:
The wind velocity is 56 m/s [W72°S]

But I don't understand how is that it ends up on the west side if both vectors were pointing east.

Welcome, @Gardunf070 !

What do you believe ends up on the West side?

W72°S is only the direction towards which the wind is blowing.
The observer on the ground feels that the wind is moving from the NE to the SW quadrant.

Not being able to see the ground as a reference, but only his instruments, the pilot believes that the airplane is moving from the SW to the NE quadrant at 50 m/s.

Simultaneously, that observer on the ground believes that the plane is moving from the NW to the SE quadrant at 30.0 m/s, although strangely, its nose points approximately towards the NE (the airplane is "crabbing").