Question

use the pythagorean theorem to find x. leave your answer as a simplified radical or as a decimal rounded to the hundredths place. draw show your work here hint: to add the square root symbol (√□), type
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Explanation:

Step1: State the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = 6\), \(c=13\), and \(b=x\).

Step2: Substitute the values into the formula

\(6^{2}+x^{2}=13^{2}\). So, \(36+x^{2}=169\).

Step3: Solve for \(x^{2}\)

\(x^{2}=169 - 36\). Then \(x^{2}=133\).

Step4: Find \(x\)

\(x=\sqrt{133}\approx11.45\) (rounded to the hundredths place).

Answer:

$11.45$