1.1.4 Manim(J): why third sidelength locked

but why should there be only one option for the third sidelength of a rectangular triangle as soon as we set 2 of its sidelengths?

1

visual: first draw a certain length of a horizonzal line in green and add the label leg a below the line, also in green, then do the same thing for another vertical line in blue, also with label, but this label is left to the line, then joint the left end of leg a, with the lower end of leg b, then draw a line from the right ending point of leg a, to the upper ending point of leg b, this line should be in orange and outside so above and at the right of this line, you add the label c, also in orange.

2

visual: wiggle first leg a and then leg b, then change the length of c, whilst maintaining all joints between the 3 lines, and maintain the length of leg a and leg b, but adjust its angle so give up the rectangularity between leg a and leg b, make c first longer and then shorter and then go back to the initial rectangular configuration

3

visual: wiggle leg and leg b simultaneously, then add a rectangle symbol between leg a and leg b, then leave all angles equal but make c longer in both directions, such that the joint constraint between right end of leg a and lower end of c is broken and the same for the joint between upper point of leg b and upper point of c, so leg a and leg b should be unaffected but make c first longer and then bring it back to its original length with the joints with leg a and leg b, then make c again longer, but this time you make c longer, the way you did in 2, using the rotation of leg a and b, away from each other, then bring leg a and b back into rectangular original configuration.