Since they are right triangles use Pythagorean Theorem. a^2 + b^2 = c^2 where c is the hypotenuse.
a. 12^2 + b^2 = 13^2 144 + b^2 = 169 subtract 144 from both sides b^2 = 25 take the square root of both sides t = 5 This is also know as a Pythagorean Triple 5-12-13
b. a^2 + 9^2 = 12^2 a^2 + 81 = 144 subtract 81 from both sides a^2 = 63 take the square root of both sides a = √63 a = √(9 * 7) a = 3√7
c. 6^2 + 9^2 = c^2 36 + 81 = c^2 117 = c^2 take the square root of each side c = √117 c = √(9*13) x = 3√13
