I didn’t label them in the drawing, but angles BDP and BCA are both right.

We are solving for the y value of P. In our drawing, P (which has the same y value of D) is at b2 + x, so we are essentially solving for x.

The first thing to notice is that these two triangles are similar.2 This means that all ratios between corresponding sides are proportional.

Many math books will make you look back and forth and back and forth and back and forth between the algebra and the drawing,3 but I will try to minimize neck cramps by using words instead of “BD ∝ BC”

Ok so, they are portional. Short leg (of small triangle) to short leg (of big triangle) is the same as long leg (of small triangle) to long leg (of big triangle). This lets us set up a proportion: