Question

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

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 \(c = 26\) ft and \(b = 10\) ft. We want to find \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 26\) and \(b = 10\) into the formula: \(a=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). First, calculate \(26^{2}-10^{2}=676-100 = 576\). Then \(a=\sqrt{576}\).

Step3: Calculate square root

\(a = 24\)

Answer:

24