To determine the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, we know one leg \(a = \sqrt{7}\) and the hypotenuse \(c = 4\). We need to find the length of the other leg \(b\).
First, we calculate \(c^2\):
\[ c^2 = 4^2 = 16 \]
Next, we calculate \(a^2\):
\[ a^2 = (\sqrt{7})^2 = 7 \]
Now we can substitute \(a\) and \(c\) into the Pythagorean theorem:
\[ \sqrt{7}^2 + b^2 = 4^2 \]
This gives us:
\[ 7 + b^2 = 16 \]
Next, we isolate \(b^2\):
\[ b^2 = 16 - 7 \]
\[ b^2 = 9 \]
Now we take the square root of both sides to find \(b\):
\[ b = \sqrt{9} = 3 \]
Thus, the length of the other leg of the right triangle is \(3\).
The correct answer is \(3\).