Geometry: Pythagorean Theorem

The Pythagorean Theorem is a formula relating the lengths of the three sides of a right triangle. It is used when we know the length of two sides of a right triangle and we need to get the length of the third side.

If we take the length of the hypotenuse to be c and the length of the legs to be a and b then this theorem tells us that:

c² = a² + b²

Example 1: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 3 inches and 4 inches.

Solution:
Step 1: Write down the formula	c2 = a2 + b2
Step 2: Plug in the values	c2 = 32 + 42
	c2 = 9 + 16
	c2 = 25
	c =
	c = 5

Answer: The length of the hypotenuse is 5 inches.

Example 2: Find the length of one side of a right triangle if the length of the hypotenuse is 10 inches and the length of the other side is 9 inches.

Solution:
Step 1: Write down the formula	c2 = a2 + b2
Step 2: Plug in the values	102 = 92 + b2
	100 = 81 + b2
Step 3: Subtract 81 from both sides	19 = b2
	b =
	b » 4.36

Answer: The length of the side is 4.36 inches.

Have a look at the following videos for an explaination of the Pythagorean Theorem and more examples on how to use the Theorem:

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