Question

find the length of the missing leg of the right triangle with a hypotenuse of 8 m and a leg of 2 m. if necessary, express your answer as a simplified square root.
60 m
2√17 m
4√15 m
2√15 m

Explanation:

Step1: Recall the Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Let the missing leg be \(x\), the given leg \(a = 2\) m, and hypotenuse \(c=8\) m. So we have the equation \(2^{2}+x^{2}=8^{2}\).

Step2: Solve for \(x^{2}\)

First, calculate \(2^{2}=4\) and \(8^{2} = 64\). Then the equation becomes \(4+x^{2}=64\). Subtract 4 from both sides: \(x^{2}=64 - 4=60\).

Step3: Simplify \(x\)

Take the square root of both sides: \(x=\sqrt{60}\). Simplify \(\sqrt{60}\) by factoring 60 as \(4\times15\), so \(\sqrt{60}=\sqrt{4\times15}=\sqrt{4}\times\sqrt{15} = 2\sqrt{15}\). So the length of the missing leg is \(2\sqrt{15}\) m.

Answer:

\(2\sqrt{15}\) m (The option: \(2\sqrt{15}\) m)