Question

what is the length of the missing leg? if necessary, round to the nearest tenth. a = feet

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 78\) and \(b = 72\), and we want to find \(a\). So, \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 78\) and \(b = 72\) into the formula: \(a=\sqrt{78^{2}-72^{2}}=\sqrt{(78 + 72)(78 - 72)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(=\sqrt{150\times6}=\sqrt{900}\).

Step3: Calculate the square - root

\(\sqrt{900}=30\).

Answer:

30