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, \(c = 6.2\) km and \(b=3.8\) km. We want to find \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

\(a=\sqrt{6.2^{2}-3.8^{2}}=\sqrt{(6.2 + 3.8)(6.2 - 3.8)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(6.2+3.8 = 10\) and \(6.2 - 3.8=2.4\). Then \(a=\sqrt{10\times2.4}=\sqrt{24}\).

Step3: Calculate and round

\(a=\sqrt{24}\approx4.9\) km.

Answer:

\(4.9\)