An aeroplane can fly at 250 km/h in still air.How long will it take it to reach a plane 500 km to south-east if a wind is blowing at 80 km/h from west?

Answer 1

Draw the diagram, head to tail (wind east, then vector down until it intercepts SE vector, and is length 250.

You have two sides (80,250) and an angle opposite the 250 side.

law of sines:
sin45/250=sinTheta/80 where Theta is the angle the still air vector intercepts the SE movement vector.
Solve Theta.
Now, the final angle, Theta1, the angle between the wind and still air vector
Theta1=180-45-Theta

Now you have the final angle,
ground speed/sinTheta1=250/Sin45

solve for ground speed.
time=500km/groundspeed