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: Write the Pythagorean theorem formula

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 10\), \(b = 13\), and \(c=x\).

Step2: Substitute the values into the formula

\(10^{2}+13^{2}=x^{2}\).

Step3: Calculate the squares

\(100 + 169=x^{2}\).

Step4: Sum the values

\(x^{2}=269\).

Step5: Solve for \(x\)

\(x=\sqrt{269}\approx16.40\) (rounded to the hundredths place).

Answer:

\(x = \sqrt{269} \approx 16.40\)