Question

find the missing side

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 78\) and \(a = 30\), and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{78^{2}-30^{2}}=\sqrt{(78 + 30)(78 - 30)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{108\times48}=\sqrt{5184}=72\).

Answer:

72