Question

find the length of the third side. if necessary, round to the nearest tenth.
24
10

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let \(a = 10\), \(c=24\), and we want to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).
Substitute the values: \(b^{2}=24^{2}-10^{2}\).
Calculate \(24^{2}=576\) and \(10^{2} = 100\). So \(b^{2}=576 - 100=476\).

Step2: Solve for \(b\)

Take the square root of \(b^{2}\), \(b=\sqrt{476}\).
\(\sqrt{476}\approx21.8\) (rounded to the nearest tenth).

Answer:

\(21.8\)