Question

find the length of the third side. if necessary, round to the nearest tenth. 11 12 answer attempt 2 out of 2 submit answer

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 11\) and \(b=12\), and we need to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 11\) and \(b = 12\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). First, calculate \(a^{2}\) and \(b^{2}\): \(a^{2}=11^{2}=121\) and \(b^{2}=12^{2} = 144\). Then, \(a^{2}+b^{2}=121 + 144=265\). So, \(c=\sqrt{265}\).

Step3: Calculate the square root and round

\(\sqrt{265}\approx16.3\) (rounded to the nearest tenth).

Answer:

\(16.3\)