What is the Pythagorean theorem and how do I use it?

Question

Accepted Answer

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side opposite the right angle) equals the sum of the squares of the other two sides. This relationship is written as a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Steps

Identify that you have a right triangle (one angle must be exactly 90 degrees).
Label the two shorter sides as 'a' and 'b', and label the hypotenuse (the side opposite the right angle) as 'c'.
Write down the formula: a² + b² = c².
Plug in the values you know into the formula.
Solve for the unknown side by using algebra: add or subtract to isolate the variable, then take the square root of both sides.

Worked example

Suppose you have a right triangle with legs of 3 and 4, and you need to find the hypotenuse. Using a² + b² = c², substitute: 3² + 4² = c². This gives 9 + 16 = c², so 25 = c². Taking the square root of both sides: c = 5. The hypotenuse is 5 units long.

Remember

The Pythagorean theorem only works for right triangles and lets you find any side length when you know the other two.

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Pythagorean Theorem Explained

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