Hello, Frostking!

An airplane is flying at 500km/hr in a wind blowing 60 km/hr toward the SE.

In what direction should the plane head to end up going due east?

What is the plane's speed relative to the ground? Code:

B
*
* | *
500 * | * 60
* |h *
* | *
* θ | 45° *
A * * * * * * * * * * C
: - - - - - - - - b - - - - - - - - :

The plane flies from to at 500 km/hr.

The wind is blowing from to at 60 m/hr.

The result flight is , directly east.

In the right triangle at the right: . [1]

In the right triangle at the left: . [2]

Substitute [1] into [2]: .

Hence: .

The direction should be about: . north of east.

We have: .

Law of Sines: .

Its ground speed is about: . km/hr.