Question

use the pythagorean theorem to find the length of the hypotenuse of the triangle below. round to two decimal places, if necessary. show your work here hint: to add the square root symbol (√□), type
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Explanation:

Step1: Write the Pythagorean theorem formula

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. Here \(a = 10\) and \(b=11\).

Step2: Substitute the values into the formula

Substitute \(a = 10\) and \(b = 11\) into \(a^{2}+b^{2}=c^{2}\), we get \(10^{2}+11^{2}=c^{2}\).
Calculate \(10^{2}=100\) and \(11^{2}=121\). Then \(100 + 121=c^{2}\), so \(c^{2}=221\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{221}\).
Using a calculator, \(\sqrt{221}\approx14.87\)

Answer:

\(14.87\)