Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 85\) km and one leg \(a = 77\) km. We want to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{85^{2}-77^{2}}=\sqrt{(85 + 77)(85 - 77)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). First, calculate \(85+77 = 162\) and \(85 - 77=8\). Then \(b=\sqrt{162\times8}=\sqrt{1296}\).

Step3: Calculate square root

\(\sqrt{1296}=36\)

Answer:

36