 Mathematics
What is the pythagorean theorem?

### 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. Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service. 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 3b 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=3b=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: Cornell University Anonymous
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