Question

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

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, \(c = 4.6\) in, one leg \(a = 4\) in, find \(b\). Rearrange formula: \(b^2 = c^2 - a^2\).

Step2: Substitute values

\(c = 4.6\), \(a = 4\), so \(b^2 = 4.6^2 - 4^2\). Calculate \(4.6^2 = 21.16\), \(4^2 = 16\). Then \(b^2 = 21.16 - 16 = 5.16\).

Step3: Solve for \(b\)

Take square root: \(b = \sqrt{5.16} \approx 2.27\) (rounded to two decimal places).

Answer:

Approximately \(2.27\) inches (or more precise \(\sqrt{5.16}\) inches)