Question

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

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 25\) and one side \(a = 7\), and we need to find \(b\).

Step2: Rearrange the formula

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

Step3: Substitute values

Substitute \(c = 25\) and \(a = 7\) into the formula: \(b=\sqrt{25^{2}-7^{2}}=\sqrt{(25 + 7)(25 - 7)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). So \(b=\sqrt{32\times18}=\sqrt{576}\).

Step4: Calculate the result

\(b = 24\)

Answer:

24