To apply the Pythagorean theorem, we start with the formula:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the other two sides.
Given that we have sides of lengths 15 and 3, it's reasonable to assume that 15 is the hypotenuse, since it is the longer of the two. Therefore, we can denote:
- \(a = 3\)
- \(c = 15\)
We need to find side \(b\). Plugging in the values into the Pythagorean theorem yields:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Subtracting 9 from both sides:
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now, taking the square root of both sides to find \(b\):
\[ b = \sqrt{216} \]
Calculating \( \sqrt{216} \):
\[ \sqrt{216} \approx 14.7 , (\text{to the nearest tenth}) \]
Thus, the unknown side length \(b\) is approximately:
\[ \boxed{14.7} \]