# Hypotenuse Theorem (Pythagorean Theorem) The "hypotenuse theorem" commonly refers to the **Pythagorean theorem**, describes the relationship between the sides of a right triangle. ## Statement For a right triangle with legs \( a \) and \( b \), and hypotenuse \( c): \[ c^2 = a^2 + b^2 \] Here, - \( c \) = length of the hypotenuse (side opposite the right angle) - \( a, b \) = lengths of the other two sides --- ## How to Solve for the Hypotenuse Given \( a \) and \( b \): \[ c = \sqrt{a^2 + b^2} \] ### Example Suppose \( a = 3 \), \( b = 4 \): \[ c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] --- ## How to Solve for a Leg If you know \( c \) and one leg: \[ a = \sqrt{c^2 - b^2} \] --- ## Visualization  *Right triangle illustration: sides \( a \) and \( b \), hypotenuse \( c \).* --- ## Summary - Use \( c^2 = a^2 + b^2 \) for right triangles. - Find the missing side by rearranging the formula as needed.