19. find the value of z.
hell

6sqrt(2)

Step-by-step explanation:

You need to use the Right Triangle Altitude Theorem.

There are two parts to this theorem.

Here is the part you need for this problem.

If the altitude is drawn to the hypotenuse of a right triangle, the length of each leg of the right triangle is the geometric mean of the segment of the hypotenuse adjacent to the leg and the entire hypotenuse.

In this case, you end up with this proportion:

Length of leg: z

Length of entire hypotenuse = 8 + 1 = 9

Length of segment of hypotenuse adjacent to leg of interest: 8

8/z = z/9

z^2 = 72

z = sqrt(72)

z = sqrt(36 * 2)

z = 6sqrt(2)