Question

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

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 legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 10\) mi and one leg \(a = 8\) mi, 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 \(c = 10\) and \(a = 8\) into the formula: \(b=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}\)

Step4: Calculate the square root

\(\sqrt{36}=6\)

Answer:

\(6\)