Day 022: Triangle Problem

I have a mathematical problem, and I hope you can understand my frustration.

2 lines drawn from ends of known leg at respective angles converge at a point

Imagine a triangle. You know the length of 1 leg, and 2 angles.

If you draw a line from each end of the known leg at their respective angles, they will converge at a definite point.

I see NO reason trigonometry needs to be used.

The core of the question is this (as I've decided): how do you convert an angle to a slope?

Every angle has a definite slope, and yes, if graphed it is the graph of tan(theta).

Maybe you can find a graph that overlays it.

But the heart of the question is how do you solve a triangle without trigonometry? You have to get creative, but if you get into it, it'll eat up hours. I know I've spent a good week's worth in the past few years.

What is my motivation? To chase what feels so right inside.

One day, I will find the answer, and if a constant is involved, I will name it after myself.