Exercise 30 Page 542

We want to find the values of $x,$ $y,$ and $z.$

Notice that $x$ and $y$ are the legs of the given right triangle, and $z$ is a partial segment of the hypotenuse divided by the altitude.

Finding $z$

Since we know the lengths of the altitude and of a partial segment of the hypotenuse, we will use the Geometric Mean (Altitude) Theorem to find the value of $z.$