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The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, the unknown side length, which is the perpendicular side to the base, represents one of the shorter sides.
Let's denote the unknown side length as $x$. We can set up the equation as follows:
$3^2 + x^2 = 15^2$
$9 + x^2 = 225$
$x^2 = 225 - 9$
$x^2 = 216$
$x = \sqrt{216}$
$x \approx 14.7$
Therefore, the unknown side length is approximately 14.7 units when rounded to the nearest tenth.