Pythagorean trigonometric identity

Ok kiddo, so Pythagorean trigonometric identity is just a fancy way of explaining how the sides of a right triangle are related to each other.

When you have a right triangle, it means that there is one angle that is exactly 90 degrees. Now, let's say we label the sides of this triangle. The side that is right across from the 90-degree angle is called the hypotenuse, and the other two sides are called the adjacent and opposite sides.

Now, here comes the fun part. The Pythagorean trigonometric identity tells us that the sum of the squares of the adjacent and opposite sides is equal to the square of the hypotenuse. That's a mouthful, isn't it?

So, if we use some letters to represent the sides, we can write the Pythagorean trigonometric identity like this:

a^2 + b^2 = c^2

See how a^2 and b^2 (the squares of the adjacent and opposite sides respectively) when added together gives you the value of c^2 (the square of the hypotenuse).

This identity is very helpful in solving problems involving right triangles. For example, if you know the value of two sides of a right triangle, you can use this identity to find the length of the third side.

Overall, the Pythagorean trigonometric identity is just a way of saying that the sides of a right triangle are related to each other in a specific and super helpful way.