Question

a right triangle has a leg length of \\(\sqrt{7}\\) and a hypotenuse length of 4. determine the length of the other leg of the right triangle. \\(\sqrt{57}\\) \\(\sqrt{49}\\) 8 3

Explanation:

Step1: Apply Pythagorean theorem

Let the other leg be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = \sqrt{7}\), \(c = 4\), and \(b=x\). So \(x^{2}+(\sqrt{7})^{2}=4^{2}\).

Step2: Simplify the equation

\(x^{2}+7 = 16\). Then \(x^{2}=16 - 7=9\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length of a side), \(x=\sqrt{9}=3\).

Answer:

3