(use the pythagorean theorem to answer the question.) an airplane takes off going straight west at 340 km/h for 1 hour, then turns and heads south for another hour at 360 km/h before reaching its final destination. what is the airplane's displacement?

South is perpendicular to West, so the plane's route forms a right triangle, and you can use Good Old Pythagoras to calculate the length of the hypotenuse.

The length of the displacement is   √(the west piece² + the south piece²)   .

That's      √ [ (340km)² + (360km)² ]

           =  √ [ (115,600) km²  +  (129,600) km² ]

           =   √ 245,200 km²

           =     495 km 

To be technical, Displacement is a vector, so we would need to
calculate its direction too.

Naturally, the plane winds up roughly southwest of where it took off.

You'd want to find the angle whose tangent is  (360/340) = about 1.059 .
The direction of the Displacement is that angle south of west. (about 46.6 degrees)