Question

a right triangle has one leg that measures 7 inches and the hypotenuse measures 23 inches. what is the length of the other leg? round your answer to the nearest hundredth, but do not include \in\ or \inches\ with your response. a tent maker wishes to support a 11-ft tent wall by attaching cable to the top of it, and then anchoring the cable 6 feet from the base? how long of a cable is needed?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Let one leg \(a = 7\), hypotenuse \(c = 23\), find the other leg \(b\). Rearrange the formula: \(b=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute values

Substitute \(a = 7\) and \(c = 23\) into the formula: \(b=\sqrt{23^{2}-7^{2}}=\sqrt{529 - 49}=\sqrt{480}\)

Step3: Calculate and round

\(\sqrt{480}\approx21.9089\), round to the nearest hundredth: \(21.91\)

Answer:

21.91