Question

calculate the exact value of the unknown side length in the right triangle.

Explanation:

Step1: Identify the formula

We use the Pythagorean theorem for a right triangle, which is \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Let the unknown leg be \(x\), the known leg is \(8\), and the hypotenuse is \(10\). So we have \(x^2 + 8^2 = 10^2\).

Step2: Solve for \(x^2\)

Calculate \(8^2 = 64\) and \(10^2 = 100\). Then \(x^2 = 100 - 64\).

Step3: Calculate \(x^2\)

\(100 - 64 = 36\), so \(x^2 = 36\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x = \sqrt{36}\).

Step5: Simplify the square root

\(\sqrt{36} = 6\).

Answer:

6