Question

An airplane has an airspeed of 650 km/h bearing 15 degrees north of west. The wind velocity of is 19 km/h in the direction of 30 degrees east of south. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

Note: I know how to solve just need help with finding the correct angles for problem.

Answer 1

Carefully draw the two vectors, placing the start of the wind vector at the end of the plane's vector. If you draw in some dotted axes, you can see that the angle between the vectors (geometric, not algebraic) is 90-30-15 = 45°

The ground speed of the plane is found using the law of cosines, since you now have SAS.

To get the direction, you need to convert to x-y components, add the two vectors and find the angle whose tangent is the resultant y/x.