Hi Welcome to MooMooMath. Today we are going to talk about one of my favorite theorems and that is the Pythagorean Theorem. The formula is A squared plus B squared, equals C squared. So let’s look at a triangle and see what this applies to. We have to have a right triangle to apply the Pythagorean Theorem, where the shorter two sides are A and B. So A and B are the two short sides or legs of a right triangle. The hypotenuse C is opposite the right triangle. So here is our example. If we have the legs 6 and 8 what is C or the hypotenuse? Let’s look at the formula in a little more detail. The rules are as follows. A and B are always the legs. C is always the hypotenuse. How do you work the formula? It is very simple. You square A ( where you get the A squared) and you square B ( where you get the B squared) then you add those two together then you take the square root of that number and you have the Pythagorean theorem. So A and B are the legs and C is always the hypotenuse. So let’s run through this example. Six and eight are both legs. So I’m going to say 6 is A and 8 is B. These can interchange, it doesn’t really matter. So we have thirty six (6 squared) plus sixty four (8 squared) and that equals C squared which is the sum of these (36 plus 64) which equals 100 and to undo a square we take the square root which equals 10. There you go and that is how you work the Pythagorean Theorem.

Find leg a in a triangle with a hypotenuse of 10 units and a leg of 8 units

In order to find the missing leg length a use the Pythagorean Theorem.

Plug in hypotenuse (10 ) and leg length ( 8 )

Take the square root of both sides

The Pythagorean Theorem states that if you square the legs of a right triangle, and add these together, it equals the hypotenuse of the right triangle squared . The Theorem can be used with right triangles in order to find the lengths of the legs and the hypotenuse.

a and b are the legs of the triangle

c is the hypotenuse and it is always opposite the right angle.

What is the hypotenuse of triangle with leg lengths of 6 and 8 units?

Pythagorean Theorem/Cut the Knot This link is a collection of 111 ways to prove the Pythagorean Theorem. Amazing,yes 111 different ways to prove the Pythagorean Theorem.