Question

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

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the unknown side be \(a\), \(c = 30\), \(b=18\). Then \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Substitute \(c = 30\) and \(b = 18\) into the formula: \(a=\sqrt{30^{2}-18^{2}}=\sqrt{(30 + 18)(30 - 18)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(=\sqrt{48\times12}=\sqrt{576}=24\)

Answer:

\(24\)