consider east-west direction along x-axis with east pointing towards positive x-axis.
consider north-south direction along y-axis with north pointing towards positive y-axis
\underset{v_{p}}{\rightarrow} = velocity of the plane = 0 i + 100 j
\underset{v_{w}}{\rightarrow} = velocity of the wind = (30 Cos315) i + (30 Sin315) j = 21.2 i - 21.2 j
net velocity of the plane is given as
\underset{v_{net}}{\rightarrow} = \underset{v_{p}}{\rightarrow} + underset{v_{w}}{\rightarrow}
\underset{v_{net}}{\rightarrow} = (0 i + 100 j) + (21.2 i - 21.2 j ) = 21.2 i + 78.8 j
t = time of travel = 3 hours
position of the plane is given as
\underset{X}}{\rightarrow} = \underset{v_{net}}{\rightarrow} t
\underset{X}}{\rightarrow} = (21.2 i + 78.8 j ) (3)
\underset{X}}{\rightarrow} = 63.6 i + 236.4 j
magnitude of distance from the initial starting point is given as
d = sqrt((63.6)² + (236.4)²) = 244.81 m
direction is given as
θ = tan⁻¹(236.4/63.6) = 75 deg north of east.