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:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg,
- \( c \) is the hypotenuse.
In this case:
- The base (one leg) is \( a = 3 \).
- The hypotenuse is \( c = 15 \).
- We need to find \( b \) (the other leg).
Plugging the known values into the Pythagorean theorem, we have:
\[ 3^2 + b^2 = 15^2 \] \[ 9 + b^2 = 225 \]
Next, we subtract 9 from both sides:
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now, we take the square root of both sides to find \( b \):
\[ b = \sqrt{216} \]
Calculating the square root gives:
\[ b \approx 14.7 \]
Rounding to the nearest tenth, the unknown side length is 14.7.
So the correct response is:
14.7