find the length of the unknown side of the triangle. the length of the unknown side of the triangle is…

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle with legs (a = 2) and (b = 6) and hypotenuse (c), the Pythagorean theorem is (c=\sqrt{a^{2}+b^{2}}). Substitute (a = 2) and (b = 6) into the formula: (c=\sqrt{2^{2}+6^{2}}).

Step2: Calculate the values inside the square root

First, calculate (2^{2}=4) and (6^{2}=36). Then (2^{2}+6^{2}=4 + 36=40). So (c=\sqrt{40}).

Step3: Simplify the square root

We can rewrite (40) as (4\times10). Then (\sqrt{40}=\sqrt{4\times10}). Using the property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}) ((a = 4), (b = 10) and (a\geq0), (b\geq0)), we get (\sqrt{4\times10}=\sqrt{4}\cdot\sqrt{10}). Since (\sqrt{4}=2), then (c = 2\sqrt{10}).

Answer:

(2\sqrt{10}\text{ ft})