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 \(c = 100\) m and \(b = 60\) m. We want to find \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 100\) and \(b = 60\) into the formula: \(a=\sqrt{100^{2}-60^{2}}=\sqrt{(100 + 60)(100 - 60)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(a=\sqrt{160\times40}=\sqrt{6400}\).

Step3: Calculate the square root

\(\sqrt{6400}=80\)

Answer:

80