Question

find the value of \c\

Explanation:

Step1: Apply Pythagorean theorem

$$a^2 + b^2 = c^2$$
Assume the two legs of the right - triangle are \(a = 4\) and \(b = 6\) (assuming the unmarked leg is \(4\) as per common problem setups for such visual representations; if only one leg \(b = 6\) is given, but in a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the formula holds). Then \(c^2=4^2 + 6^2\).

Step2: Calculate \(c^2\)

$$c^2=16 + 36=52$$

Step3: Find \(c\)

$$c=\sqrt{52}$$

Answer:

\(c = \sqrt{52}\) (the orange - colored option)