Pythagorean TheoremBy now you are able to find the area of a triangle, surface area of a triangle and the volume of a triangular prism. All of these formulas deal with the space of a triangle, but what about the sides.

The Pythagorean Theorem allows you to find any of the given sides of a right triangle. Thinking back to our angle unit a right triangle is a triangle with a 90 degree angle.

Pythagorean Theorem Continued

• The Pythagorean Theorem comes to us from the Greeks. Credit is given to a man named Pythagoras (570 BC – 495 BC.) It is possible that he wasn’t the one who actually came up with the formula.

a + b = c

So where is it used?

• The Pythagorean Theorem is used anytime you know two sides of a triangle but not the third. Some examples are pitching a tent and needing to know how long a rope needs to be to tie it to the ground. Another example might be archery when trying to make an up hill shot. Perhaps you are building a house and need to figure out how long the trusses need to be.

a + b = c

How do you use it.a + b = c

4+ 6 = c

16+ 36 = 52

c = 52

Where does it come from

• As you can see the area of the square labeled see is the size of a and b added. This is where the formula comes from.

What is the square root of 52?• Remember that when we take a number to the second

power we have multiplied that number by itself. The inverse of taking a number to a power is to find the root of the result. Therefore what two numbers multiplied by each other result in 52.

In this case we know that it would be between 7 and 8, because 7 X 7 =49 and 8 X 8 = 64.

Challenge keep trying numbers between 7 and 8 to see if you can find an exact answer, or is the answer irrational such as the square root of 2?

Application

• Last week you began building a floor plan. This week I would like you to design your roof. Using the Pythagorean theorem please design a roof system for your house.

• What will the total cost be of the roof. Don’t worry about staying in your budget for this one.