If \(\cot(\theta) = \frac{8}{15}\), where \(\theta\) is an acute angle, we can use the definition of the cotangent function to find the value of \(\sin(\theta)\). The cotangent function is defined as the reciprocal of the tangent function: \(\cot(\theta) = \frac{1}{\tan(\theta)}\). The tangent function, in turn, is defined as the ratio of the opposite side to the adjacent side in a right triangle: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).

Since \(\cot(\theta) = \frac{8}{15}\), we have \(\frac{1}{\tan(\theta)} = \frac{8}{15}\), which means that \(\tan(\theta) = \frac{15}{8}\). This tells us that in a right triangle with angle \(\theta\), the ratio of the opposite side to the adjacent side is \(\frac{15}{8}\). We can use this information to find the length of the hypotenuse using the Pythagorean theorem: \(\text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2\). Plugging in the values for the opposite and adjacent sides, we get:

\(\text{hypotenuse}^2 = 15^2 + 8^2 = 225 + 64 = 289\)

Taking the square root of both sides, we find that the length of the hypotenuse is \(\sqrt{289} = 17\).

Now that we know the lengths of all three sides of the right triangle, we can use the definition of the sine function to find the value of \(\sin(\theta)\). The sine function is defined as the ratio of the opposite side to the hypotenuse in a right triangle: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\). Plugging in the values for the opposite side and hypotenuse, we get:

\(\sin(\theta) = \frac{15}{17}\)

So, if \(\cot(\theta) = \frac{8}{15}\), where \(\theta\) is an acute angle, then \(\sin(\theta) = \frac{15}{17}\).