To find the unknown side length of the right triangle using the Pythagorean Theorem, we can apply the formula:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg of the triangle (the base),
- \( b \) is the other leg of the triangle (the perpendicular side),
- \( c \) is the hypotenuse.
From the information provided:
- \( a = 3 \)
- \( c = 15 \)
We need to find \( b \).
Plugging the values into the Pythagorean theorem:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Now, isolate \( b^2 \) by subtracting 9 from both sides:
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{216} \]
Calculating the square root:
\[ b \approx 14.7 \]
Rounding to the nearest tenth, the unknown side length is approximately \( 14.7 \).
Thus, the correct response is 14.7.