Pythagorean Theorem

The Formula

For a right triangle with legs $a$ and $b$ and hypotenuse $c$: $a^2 + b^2 = c^2$

Remember:

• The hypotenuse is the longest side
• The hypotenuse is opposite the right angle
• The legs form the right angle

Finding the Hypotenuse

If you know both legs: $c = \sqrt{a^2 + b^2}$

Example: Legs are 3 and 4 $c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

Finding a Leg

If you know the hypotenuse and one leg: $a = \sqrt{c^2 - b^2}$

Example: Hypotenuse is 13, one leg is 5 $a = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12$

Real-World Applications

• Finding distances
• Construction and building
• Navigation
• Screen sizes (diagonal measurement)