Hello, ewojmath1!

I have a different interpretation of your wording.

The legs of a right triangle are 6 and 8.

(a) What is the length of the median to the hypotenuse ?

(b) What is the length of the altitude to the hypotenuse ?

Using Pythagorus: .

Code:

*
* \ *
6 * \ * 8
* \ *
* \ *
* \ *
* - - - - - * - - - - - *
5 5

The right triangle can be inscribed in a semicircle of radius 5.

Since the median to hypotenuse is also a radius, its length is 5.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Let be the altitude to the hypotenuse.

Code:

C
*
*| *
6 * | * 8
* |h *
* | *
* |D *
A * - - * - - - - - - - - * B
10

Since , we have: .