find the length of the third side. if necessary, round to the nearest tenth. answer attempt 1 out of 2

Answer

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c) is the hypotenuse. Here (c = 30) and (a=18), and we want to find (b).

Step2: Rearrange the formula

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

Step3: Substitute values

Substitute (c = 30) and (a = 18) into the formula: (b=\sqrt{30^{2}-18^{2}}=\sqrt{(30 + 18)(30 - 18)}) (using (x^{2}-y^{2}=(x + y)(x - y))). Then (b=\sqrt{48\times12}=\sqrt{576}).

Step4: Calculate the result

(b = 24).