Question

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

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, \(c = 90\) cm and \(a = 54\) cm, and we want to find \(b\). So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{90^{2}-54^{2}}=\sqrt{(90 + 54)(90 - 54)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(90+54 = 144\) and \(90 - 54=36\). Then \(b=\sqrt{144\times36}\). Since \(\sqrt{144\times36}=\sqrt{144}\times\sqrt{36}\), and \(\sqrt{144}=12\), \(\sqrt{36}=6\), so \(b = 12\times6=72\) cm.

Answer:

72