If we know the sides of a triangle - we can always use the Pythagorean Theorem backwards in order to determine if we have a right triangle, this is called the converse of the Pythagorean Theorem.

If a2 + b2 = c2 then △ABC is a right triangle.

When working with the Pythagorean theorem we will sometimes encounter whole specific numbers that always satisfy our equation - these are called a Pythagorean triple. One common Pythagorean triple is the 3-4-5 triangle where the sides are 3, 4 and 5 units long.

There are some special right triangles that are good to know, the 45°-45°-90° triangle has always a hypotenuse v2 times the length of a leg. In a 30o-60o-90° triangle the length of the hypotenuse is always twice the length of the shorter l.eg and the length of the longer leg is always v3 times the length of the shorter leg.

Video lesson: Find the value of x in the right triangle.

To see the solution look at the video in the next page.

Here we have a right triangle and we want to solve for this unknown side x and since it is a right triangle we can use Pythagoras' theorem and do that accordingly. So we need the square of this side plus the square of this side is equal to the square of this hypotenuse. So x2 = 122 = 142 and we’re just going to solve for x. So we can move this to the other side. X2 = 142 – 122 , we can expand this out and get something over here, X2 = 142 is 196 minus 122 is a dozen dozen which is 144. This difference is x2 = 52 and then we can take the square root of both sides to solve for x finally. X equals √52 and that’s about 7.2.