The height of a triangle is 9, the length is 5, what is the third side?

Use the Pythagorean Theorem to solve for the third side. The third side must be the hypotenuse since the height (vertical leg) is 9, and the length (horizontal leg) is 5.

a² + b² = c², where a and b are the legs and c is the hypotenuse. Plug in 5 and 9 for a and b; solve for c.

5² + 9² = c² ⇒ 25 + 81 = c²

106 = c²

Square root both sides.

c = 10.3

Third side: 10.3