Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 7\) miles and \(b = 5\) miles, and we want to find \(a\). So, \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

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

Step3: Simplify and round

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

Answer:

\(4.9\)