Question

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

Explanation:

Step1: Identify the triangle type

It is a right - triangle. Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(c = 30\) and \(a=18\), and we need to find \(b\).

Step2: Rearrange the Pythagorean theorem

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

Step3: Substitute the values

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

Step4: Calculate the value of \(b\)

\(b = 24\)

Answer:

24