Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(c = 95\) m and \(a = 57\) m, and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 95\) and \(a = 57\) into the formula: \(b=\sqrt{95^{2}-57^{2}}=\sqrt{(95 + 57)(95 - 57)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(95+57 = 152\) and \(95 - 57=38\). Then \(b=\sqrt{152\times38}=\sqrt{5776}\).

Step3: Calculate square - root

\(\sqrt{5776}=76\)

Answer:

76