Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b\) is the unknown side, and \(c = 24\). Let the unknown side be \(x\). Then \(x=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

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

Step3: Calculate the square root

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

Answer:

\(21.8\)