Question

the hypotenuse of a right triangle is 6 inches and one of the legs is \\( \sqrt { 6 } \\) inches, the exact value of the other leg is ______ inches. a) 15 b) \\( \sqrt { 30 } \\) c) \\( \sqrt { 15 } \\) d) 30

Explanation:

Step1: Apply Pythagorean theorem

Let the other leg be \(x\). By \(a^{2}+b^{2}=c^{2}\) (where \(c\) is hypotenuse, \(a,b\) are legs), we have \(x^{2}+(\sqrt{6})^{2}=6^{2}\).

Step2: Simplify the equation

\(x^{2}+6 = 36\). Then \(x^{2}=36 - 6=30\).

Step3: Solve for \(x\)

Take square root of both sides: \(x=\sqrt{30}\) (since length \(x>0\)).

Answer:

B. \(\sqrt{30}\)