Could someone please help with this question for math!!!!!?

Question

Low-voltage lighting is a popular feature of landscaping. Two pathways meet at 30 degrees to each other. One pathway has the lighting, and the first light is placed where the two paths meet. The distance between successive lights is 5m, and each has a range of effective illumination of 6m. For the second pathway, find, to the nearest tenth of a metre, the length that is
a.) effectively illuminated
b.) effectively illuminated by both the second and third light
c.) effectively illuminated by the third or fourth light.
Please show all workings.

Answer 1

Here are some hints:
1. The limit of illumination of each light is a circle of radius 6.
2. The farthest distance (x_max) down the first path that a light could be and still illuminate at least one point will have it's circle tangent to the 2nd path and will be a distance 6 from the 2nd path. Hence 6/x_max = sin(30). Lights at position x>x_max will not illuminate and can be ignored.
3. For positions 6 4. For light positions 0
You should be able to grind it out from here. Hope this helps.