**Final Answer: b) 49.02 N**
**Explanation:**
The frictional force acting on the child can be calculated using the formula: \( F_{\text{friction}} = \mu \cdot F_{\text{normal}} \), where \( \mu \) is the coefficient of friction and \( F_{\text{normal}} \) is the normal force. The normal force can be found using the equation: \( F_{\text{normal}} = m \cdot g \cdot \cos(\theta) \), where \( m \) is the mass of the child, \( g \) is the acceleration due to gravity, and \( \theta \) is the angle of the slide.
Given that the child's mass (\( m \)) is 30.0 kg, the angle (\( \theta \)) is 60.0°, the coefficient of friction (\( \mu \)) is 0.250, and the acceleration due to gravity (\( g \)) is approximately 9.8 m/s², we can substitute these values into the equations.
First, calculate the normal force using \( F_{\text{normal}} = m \cdot g \cdot \cos(\theta) \):
\[ F_{\text{normal}} = 30.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot \cos(60.0^\circ) \]
Now, substitute \( F_{\text{normal}} \) into the frictional force equation:
\[ F_{\text{friction}} = 0.250 \cdot F_{\text{normal}} \]
After performing the calculations, the frictional force is approximately 49.02 N, making option b) the correct answer.