Question

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

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 \(c = 50\) m and \(b=14\) m, and we want to find \(a\). So \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 50\) and \(b = 14\) into the formula: \(a=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(50+14 = 64\) and \(50 - 14=36\), so \(a=\sqrt{64\times36}\). Then, \(\sqrt{64\times36}=\sqrt{64}\times\sqrt{36}=8\times6 = 48\) m.

Answer:

48