Try this Drag the orange dots on each vertex
of the right triangle below. The formula showing the calculation of the Pythagorean Theorem will change accordingly.
Although Pythagoras' name is attached to this theorem,
it was actually known centuries before his time by the Babylonians.
There are many proofs of this theorem,
some graphical in nature and others using algebra.
See A graphical proof of the Pythagorean Theorem for one such proof.
On the web site "cut-the-knot",
the author collects proofs of the Pythagorean Theorem, and as of
this writing has listed over 70, but hundreds are actually known.
Solving the right triangle
The term "solving the triangle" means that if we start with a right triangle and know any two sides, we can find, or 'solve for', the unknown side.
This involves a simple re-arrangement of the Pythagoras Theorem formula to put the unknown on the left side of the equation.
Find the hypotenuse
If we know the two legs of a right triangle we can solve for the hypotenuse using the formula: