Question 576622
Let h be the altitude to the hypotenuse. Using the area for a triangle, we have


*[tex \LARGE \frac{AB}{2} = \frac{Ch}{2} \Rightarrow AB = Ch \Rightarrow h = \frac{AB}{C}].


By the Pythagorean theorem, *[tex \LARGE C = \sqrt{A^2 + B^2}] so


*[tex \LARGE h = \frac{AB}{\sqrt{A^2 + B^2}}]