To find the unknown side length in the right triangle using the Pythagorean theorem, we can apply the following formula:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is one leg (base),
- \( b \) is the other leg (perpendicular side),
- \( c \) is the hypotenuse.
Given:
- \( a = 3 \) (base),
- \( c = 15 \) (hypotenuse),
- \( b \) is the unknown side.
Plug in the known values:
\[ 3^2 + b^2 = 15^2 \]
This simplifies to:
\[ 9 + b^2 = 225 \]
Now, subtract 9 from both sides:
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now, 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 answer is:
14.7