The resultant velocity of the plane is 275.5 mph at a direction of 60.7 degrees south of west.
How to solve
1. Convert wind velocity to components:
Northward component

Eastward component

2. Convert plane velocity to components:
Westward component

Southward component

3. Combine wind and plane components:
Resultant eastward velocity

Resultant northward velocity (V_rn) = V_n - V_s = 28.6 mph - 260.1 mph = -231.5 mph (negative indicates southward direction)
4. Calculate resultant magnitude:
Resultant velocity (V_r) =

5. Calculate resultant direction:
Inverse tangent of (V_rn / V_re) =

Therefore, the resultant velocity of the plane is 275.5 mph at a direction of 60.7 degrees south of west.
The Complete Question
A plane flies in a direction of 24.5 degrees south of west at 290 mph. It encounters a 30.5 mph wind that is heading 21 degrees east of north. What is the resultant velocity of the plane (magnitude and direction)?