Geometry problem

I need someone to help me with what is essentially a geometry problem. I want to build a spreadsheet that solves for the apparent wind a windsurfer experiences when jibing (changing from sailing across the wind in one direction to the opposite direction by turning the front of the board downwind). This will be a function of two vectors: 1) the true wind (which we will consider constant throughout), and 2) the induced wind (which will be exactly opposite the direction and velocity of the board at various points in the turn). I've played with this enough to see that it comes down to solving for the angle and length of a line dissecting a parallelogram representing the two vectors. This spreadsheet contains images and notes: https://docs.google.com/spreadsheets/d/1epTgfDOUyFoGtfFsFszMtIoq2zoYP7X3pwXbufazZ8Y/edit#gid=0 In the parallelogram image, Line A would represent the true wind, and would be assumed to be fixed in both velocity and direction. Line B would be the induced wind which would be exactly equal to the negative of the speed and angle of the windsurf board at each point of the turn. The speed and velocity of vector B (essentially the board speed and angle) would be variables input by me for each of 10 points in the turn. I want to solve for the length of the red line and θ for each of the 10 points, which would represent the apparent wind experienced by the windsurfer.