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To solve this problem, we can use trigonometry.
Let's label the variables:
- Distance from the light to the bike path = x (unknown)
- Distance from the light to the 150m sight line = 120m
- Angle between the sight line and the bike path = 23 degrees
We can use the sine function to find x:
sin(23 degrees) = opposite/hypotenuse
The opposite side is x, and the hypotenuse is 120m. Hence:
sin(23 degrees) = x/120
Multiply both sides by 120:
120 * sin(23 degrees) = x
x ≈ 47.016
Therefore, the length of the bike path that is effectively illuminated by the light is approximately 47 meters.