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

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse (c) and legs (a) and (b), (a^{2}+b^{2}=c^{2}). Here, the hypotenuse (c = 20) km and one leg (a = 16) km, and we need to find the other leg (b).

Step2: Rearrange the Pythagorean theorem

We can rearrange the formula to solve for (b): (b=\sqrt{c^{2}-a^{2}})

Step3: Substitute the values

Substitute (c = 20) and (a = 16) into the formula: (b=\sqrt{20^{2}-16^{2}}=\sqrt{400 - 256}=\sqrt{144})

Step4: Calculate the square root

(\sqrt{144}=12)

Answer:

(12)