Question

orean theorem. round
u 6 ft v
?
9 ft
w
v =

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let \(UW = a\), \(UV=b = 6\) ft and \(WV=c = 9\) ft. We want to find \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(b = 6\) and \(c = 9\) into the formula: \(a=\sqrt{9^{2}-6^{2}}=\sqrt{81 - 36}=\sqrt{45}\).

Step3: Simplify the square - root

\(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx3\times2.236 = 6.708\approx6.7\) ft.

Answer:

\(6.7\) ft