I dont think you can assume that there will be a 90deg angle between spi-pole and mast. Mast rake and spi-pole height will influence this, so a*a=b*b+c*c might not be correct.

The picture is of a Gran Segel mk-4 Tornado spi. Luff length on this spi is 9130mm while distance from bearing point on the spi-pole to bearing point at the mast is 9100mm. Max allowed luff length in the Tornado class is 9150mm. I just tought it was a good picture showing how they do the luff of their very good spis.
It's definately what the sailmaker do with the allotted geometry that is important. E.g. last week I learnt that the radial panels should not be wider than 6deg. More than that and the cloth would not be able to withstand the bias loads in strong winds and the surface would be uneven = more drag, less good shape and shorter lifetime of the sail. This means that more panels are needed, but this brings the price up..

I find the subject of sail trim and design wildly interesting. It's very rewarding when sailing to know the whats, wheres and whys of the sailshapes you want for different conditions. It's a bit surprising that so few participate and show interest when these discussions pop up from time to time.