Question

use the pythagorean theorem to find x and y in each of the following. complete parts (a) through (f) below

(simplify your answer. type an exact answer, using radicals as needed. type an expression using s as the variable. use integers or fractions for any numbers in the expression.)

and
(simplify your answers. type exact answers, using radicals as needed.)

and
(simplify your answers. type exact answers, using radicals as needed.)

Explanation:

Step1: Find \( y \) using the Pythagorean theorem

In a rectangular prism, for the base - level right - triangle (with sides \( 25 \) and \( 9 \)), by the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Here \( a = 25 \), \( b = 9 \), and \( y \) is the hypotenuse. So \( y=\sqrt{25^{2}+9^{2}}=\sqrt{625 + 81}=\sqrt{706} \).

Step2: Find \( x \) using the Pythagorean theorem

Now, consider the right - triangle with sides \( y=\sqrt{706} \) and \( 15 \). Using the Pythagorean theorem \( x=\sqrt{y^{2}+15^{2}} \). Substitute \( y^{2}=706 \), then \( x=\sqrt{706+225}=\sqrt{931} \).

Answer:

\( x=\sqrt{931}\) and \( y = \sqrt{706}\)