Question

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

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, \(c = 20\) m and \(a=12\) m. We want to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 20\) and \(a = 12\) into the formula: \(b=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{32\times8}=\sqrt{256}\).

Step3: Calculate the square root

\(b = 16\) m.

Answer:

16