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

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 = 20) yd and (b = 16) yd, and we want to find (a). So, (a=\sqrt{c^{2}-b^{2}}).

Step2: Substitute values

Substitute (c = 20) and (b = 16) into the formula: (a=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}) (using the difference - of - squares formula (x^{2}-y^{2}=(x + y)(x - y))). Then (a=\sqrt{36\times4}=\sqrt{144}).

Step3: Calculate the square root

(a = 12) yd.

Answer:

12