To find the unknown side length of the right triangle using the Pythagorean Theorem, we can use the formula:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs of the triangle,
- \(c\) is the length of the hypotenuse.
In this case:
- The base \(a = 3\),
- The hypotenuse \(c = 15\),
- The unknown side \(b\) is what we need to find.
Substituting the values into the Pythagorean theorem:
\[ 3^2 + b^2 = 15^2 \]
Calculating \(3^2\) and \(15^2\):
\[ 9 + b^2 = 225 \]
Now, isolate \(b^2\):
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now take the square root of both sides to find \(b\):
\[ b = \sqrt{216} \approx 14.6969 \]
Rounding to the nearest tenth, we find:
\[ b \approx 14.7 \]
Thus, the length of the unknown side is:
14.7