Exercise 20 Page 465

Let's analyze the given right triangle so that we can find the values of $x$ and $y.$

Consider the bigger triangle. We know an expression for the length of the shorter leg, an expression for the altitude, and the lengths of two segments of the hypotenuse. Therefore, we can use the corollaries of the Right Triangle Similarity Theorem to write two proportions. Let's do it!

Finding $x$

To find the value of $x,$ we will use the following corollary of the Right Triangle Similarity Theorem.