An airplane flies horizontally from east to west at 280280 mi/hr relative to the air. if it flies in a steady 3030 mi/hr wind that blows horizontally toward the southwest (45degrees° south of west), find the speed and direction of the airplane relative to the ground.

We can find for the new speed of the plane using the cosine law. Let us say that the new speed is c:

c^2 = 280^2 + 30^2 - 2 (280) (30) cos (90°+45°)

c = 302 mi/hr

The angle relative to the ground is calculated using sine law:

sin C / 30 = sin (90+45) / 302

C = 4.03°

The new speed is 302 mi/hr at - 4.03° relative to the ground.