question\nfind the length of the third side. if necessary, round to the nearest tenth.\nanswer attempt 1 out…

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c) is the hypotenuse. Here, (c = 21) and (a = 11), and we want to find (b).

Step2: Rearrange the formula

We get (b=\sqrt{c^{2}-a^{2}}).

Step3: Substitute values

Substitute (a = 11) and (c = 21) into the formula: (b=\sqrt{21^{2}-11^{2}}=\sqrt{(21 + 11)(21 - 11)}) (using (x^{2}-y^{2}=(x + y)(x - y))). So (b=\sqrt{32\times10}=\sqrt{320}).

Step4: Calculate and round

(\sqrt{320}\approx17.9).

Answer:

17.9