Question

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

Explanation:

Step1: Identify triangle type

It's a right - triangle, so we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, \(c = 24\), \(b=10\), we need to find \(a\).
Rearranging the formula for \(a\): \(a=\sqrt{c^{2}-b^{2}}\)

Step2: Substitute values

Substitute \(c = 24\) and \(b = 10\) into the formula:
\(a=\sqrt{24^{2}-10^{2}}=\sqrt{576 - 100}=\sqrt{476}\)

Step3: Calculate and round

Calculate \(\sqrt{476}\approx21.8\) (rounded to the nearest tenth)

Answer:

\(21.8\)