Question

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

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 \(c = 65\) yd and \(a = 56\) yd. We want to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 65\) and \(a = 56\) into the formula: \(b=\sqrt{65^{2}-56^{2}}=\sqrt{(65 + 56)(65 - 56)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(65+56 = 121\) and \(65 - 56=9\). Then \(b=\sqrt{121\times9}\).

Step3: Calculate square - root

Since \(\sqrt{121\times9}=\sqrt{121}\times\sqrt{9}\), and \(\sqrt{121}=11\), \(\sqrt{9}=3\), so \(b = 11\times3=33\) yd.

Answer:

33