Question

28,725 Learners found this answer helpful

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:

\(12\)