Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (\(c = 7\) cm) and \(a = 5\) cm. We need to find \(b\). Rearranging the formula gives \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 7\) and \(a = 5\) into the formula: \(b=\sqrt{7^{2}-5^{2}}=\sqrt{49 - 25}=\sqrt{24}\).

Step3: Simplify

\(\sqrt{24}\approx4.9\) (rounded to the nearest tenth).

Answer:

\(4.9\) centimeters