a light in a park can illuminate effectively up to a distance of 120m. the 150m sight line to the light makes an angle of 23 degrees with the bike path. determine the length of the bike path to the nearest metre, that is effectively illuminated light by the light.
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.