### Question Description

I need help with a Mathematics question. All explanations and answers will be used to help me learn.

Explain what the theorem is and show an example of how it can be applied.

## Final Answer

The **pythagorean theorem **is a formula relating the sides of a right triangle derived by a Greek mathematician named Pythagorus in the **500s BC**. The formula works for all right triangles with sides of **a, b, and c** where c is the **hypotenuse**, or side opposite the right angle.

The formula he derived was known as the **pythagorean theorem**:

**a^2+b^2=c^2 **(The ^2 means an exponent of 2, or squared).

This is read as **a squared + b squared = c squared**.

For example, if there was a right triangle with the sides of 3, 4, and 5, then **a would be 3**, **b would be 4**, and **c would be 5**.

Plug this into the formula, and it works!

**3^2+4^2=5^2**. Simplifying the squares, we get:

**9+16=25**. Simplifying by addition, we get the true statement:

**25=25**.

The **pythagorean theorem **can be applied in numerous ways, and here I'll give an example. Let's say you have a TV and you need to find the length of the diagonal going across. You know that the sides are exactly **3 feet **by **5 feet**. It doesn't matter which you make a or b, so let's make:

**a=3**, **b=5**. We want to find c, the unknown variable, the diagonal. Plug this into the equation and get:

**3^2+5^2=c^2**. Simplify the squares and get:

**9+25=c^2**. Simplify this using addition and get:

**34=c^2**. Now, we need to solve for c. C squared equals 34, so we need to take the square root of 34. Using a calculator, we can approximate:

**c=5.83095...**

So, using the Pythagorean theorem, we found that the hypotenuse was about 5.8 feet!

Hope this helped, thanks!

Here's a good visualization of the **Pythagorean Theorem:**

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