Question

use the pythagorean theorem to find x and y in each of the following. complete parts (a) through (f) below.
a. x = 8
(simplify your answer. type an exact answer, using radicals as needed.)
b. x =
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the legs. For part (b), \(a = 3\), \(b = 4\), and \(c=x\).

Step2: Substitute values into the formula

Substitute \(a = 3\) and \(b = 4\) into \(a^{2}+b^{2}=c^{2}\). We get \(3^{2}+4^{2}=x^{2}\).
Calculate \(3^{2}=9\) and \(4^{2}=16\). Then \(9 + 16=x^{2}\), so \(x^{2}=25\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{25}\).

Answer:

\(x = 5\)