How to measure changing dimensions of right scalene triangle as hypotenuse rotates?

This is a high school level geometry question.

As shown in the top half of the image below, suppose we start with a right scalene triangle with hypotenuse = 5 and sides b and c = to 3 and 4, respectively.

Suppose we begin rotating the hypotenuse outward (rotated hypotenuse shown as dashed line "d" in bottom half of image). We rotate hypotenuse line "d" out by a unit of 1 from angle "B", denoted as dashed line "e" in the image. How do we measure lines f and g, formed in the new triangle as line d rotates outward?

It's obvious to me the new angle D formed as line "d" rotates will <> angle B. The little black square in the new triangle formed is my recollection of a 90 degree angle designation.

Solution 1:

You have two equations for $f$ and $g$: $$ f:(4+g)=1:3 $$ (from triangle similarity) and $$ f^2+1=g^2 $$ (from Pythagoras' theorem).