To help us solve the problem we draw each displacement given in the problem as a vector on the plane:
Now, we know that the components of a vector are given by:
For the 620 km displacement, we know that its magnitude is 620 km and its angle is 240° (with respect to the x-axis in the direction stated above), then we have:
For the 290 km the displacement, we know that its magnitude is 290 km and its angle is 115°, then we have:
Now, the total displacement of the plane is the sum of this two vectors then we have:
Hence, the displacement of the plane is:
Finally we get the magnitude of the vector:
Therefore, the displacement of the plane is 512.1 km