To find the unknown side length of the right triangle using the Pythagorean Theorem, we 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 triangle:
- The base (one side) \( a = 3 \),
- The hypotenuse \( c = 15 \),
- The perpendicular side \( b \) is unknown.
Plugging the values into the Pythagorean theorem:
\[ 3^2 + b^2 = 15^2 \] \[ 9 + b^2 = 225 \]
Now, isolate \( b^2 \):
\[ b^2 = 225 - 9 \] \[ b^2 = 216 \]
Now, take the square root to find \( b \):
\[ b = \sqrt{216} \]
Calculating the square root:
\[ b \approx 14.7 \]
Therefore, the nearest tenth value of the unknown side length is:
14.7