Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here \(a = 11\), \(b=11\).

$$c=\sqrt{11^{2}+11^{2}}$$

Step2: Calculate the squares

\(11^{2}=121\), so \(11^{2}+11^{2}=121 + 121=242\)

$$c=\sqrt{242}$$

Step3: Simplify the square root

\(\sqrt{242}=\sqrt{121\times2}=11\sqrt{2}\approx11\times1.414 = 15.6\)

Answer:

\(15.6\)