Question

1. find the value of x.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(x^{2}+6^{2}=10^{2}\).

Step2: Simplify the equation

\(x^{2}+36 = 100\). Then, \(x^{2}=100 - 36\).

Step3: Calculate \(x^{2}\)

\(x^{2}=64\).

Step4: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents a length (non - negative), \(x=\sqrt{64}\).

Answer:

\(x = 8\) mi