To find the magnitude of the resultant velocity of the plane, we can use vector addition.
Given:
Velocity of the plane (in the north direction) = 372.32 km/h, N
Velocity of the crosswind (in the west direction) = 76.66 km/h, W
Since the velocities are in different directions, we can consider them as vectors. To find the resultant velocity, we can use the Pythagorean theorem.
The magnitude of the resultant velocity can be calculated using the formula:
Resultant velocity = √(velocity of the plane)^2 + (velocity of the crosswind)^2
Resultant velocity = √(372.32^2 + 76.66^2)
Resultant velocity ≈ √(138652.7424 + 5879.3156)
Resultant velocity ≈ √(144532.058)
Resultant velocity ≈ 380.2 km/h
Therefore, the magnitude of the resultant velocity of the plane is approximately 380.2 km/h.