You're on the right track with respect to breaking the components of velocity into horizontal and vertical pieces. It helps to draw out a sketch - see below.

First, you gave the angle of the wind as 30 degrees west of north, which means it is 60 degrees from teh horizontal axis. The horizontal component of the wind is therefore -35m/s x cos(60) = -17.5 m/s, and the vertical component is 35 m/s x sin(60) = 30.31 m/s. So that was the first problem - you had these reversed. Note the minus sign for the horizontal piece - that's because it is the west (left). The horizontal component of the wind is +100 m/s, and the vertical component is 0 m/s - since the plane is heading due east. Now add the horoizontal pieces and then the vertical pieces:

V_h = 100 - 17.5 = 82.5m/s

V-v = 30.31 m/s

The total velocity is found using the Pythagorian theorem:

V_t = sqrt (V_h^2 + V_v^2) = sqty (82.5^2 + 30.31^2) = 87.9 m/s

Hope this helps.