Question

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

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, \(c = 5\) km and \(b=2\) km, and we want to find \(a\). So, \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 5\) and \(b = 2\) into the formula: \(a=\sqrt{5^{2}-2^{2}}=\sqrt{25 - 4}=\sqrt{21}\).

Step3: Calculate and round

\(\sqrt{21}\approx4.6\) km.

Answer:

4.6