To find the unknown side length in the right triangle using the Pythagorean Theorem, we can start with the theorem itself, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.
In this case, we have:
- \( c = 15 \)
- \( a = 3 \)
- \( b = ? \)
We will substitute \( a \) and \( c \) into the equation:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Now, we will isolate \( b^2 \):
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now, we will take the square root of both sides to find \( b \):
\[ b = \sqrt{216} \]
Now, we can calculate \( \sqrt{216} \):
\[ b \approx 14.7 \]
Rounding 14.7 to the nearest tenth, the final answer is:
14.7