Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 8.8\) ft and \(a=8.5\) ft. We need to find \(b\). So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 8.8\) and \(a = 8.5\) into the formula: \(b=\sqrt{8.8^{2}-8.5^{2}}=\sqrt{(8.8 + 8.5)(8.8 - 8.5)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
First, calculate \(8.8+8.5=17.3\) and \(8.8 - 8.5 = 0.3\). Then \(b=\sqrt{17.3\times0.3}=\sqrt{5.19}\).

Step3: Calculate the square - root

\(\sqrt{5.19}\approx2.3\)

Answer:

\(2.3\)