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 ($\sqrt{\square}$), type
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 17\), \(b = 13\), and \(a=x\). So \(x^{2}+13^{2}=17^{2}\).

Step2: Simplify the equation

\(x^{2}+169 = 289\). Then \(x^{2}=289 - 169\).

Step3: Calculate \(x^{2}\)

\(x^{2}=120\).

Step4: Solve for \(x\)

\(x=\sqrt{120}\). Simplify \(\sqrt{120}=\sqrt{4\times30}=2\sqrt{30}\approx10.95\) (rounded to the hundredths place).

Answer:

\(x = \sqrt{120} \approx 10.95\)