Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
( b = ) (\boxed{}) feet

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is hypotenuse, \(a\) and \(b\) are legs. Here, \(c = 8.8\) ft, \(a = 8.3\) ft, find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(c = 8.8\), \(a = 8.3\), so \(c^{2}=8.8^{2}=77.44\), \(a^{2}=8.3^{2}=68.89\). Then \(c^{2}-a^{2}=77.44 - 68.89=8.55\).

Step3: Take square root

\(b=\sqrt{8.55}\approx2.9\) (rounded to nearest tenth).

Answer:

\(2.9\)