Question

use the pythagorean theorem to find x and y in each of the following. complete parts (a) through (f) below.
a. x = □
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 17\), \(a=15\), and \(b = x\). So, \(15^{2}+x^{2}=17^{2}\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{64}\).

Answer:

\(8\)