To find the unknown side length of the right triangle using the Pythagorean theorem, you can use the formula:
\[ a^2 + b^2 = c^2 \]
Where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.
In this case,
- Hypotenuse \( c = 15 \)
- Base \( a = 3 \)
- Perpendicular side \( b = ? \)
Plugging the values into the theorem:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Now, subtract 9 from both sides:
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Next, take the square root of both sides:
\[ b = \sqrt{216} \]
Calculating \( \sqrt{216} \):
\[ \sqrt{216} \approx 14.7 \]
So, the length of the unknown side is approximately 14.7. Rounding to the nearest tenth gives you:
14.7
Therefore, the correct response is 14.7.