in the figure below, find the exact value of z. (do not approximate your answer.)

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if an altitude is drawn from the right - angle to the hypotenuse, then (z^{2}=6\times8).

Step2: Calculate the value of (z)

Since (z^{2}=48), then (z = \sqrt{48}). Simplifying, (z=\sqrt{16\times3}=4\sqrt{3}).

Answer:

(4\sqrt{3})