two pathways meet at 30 degrees to eachother. one pathway has lighting and the other does not. the distance between successive lights on the lighted pathway is 5 meters. each light has a range of effective illumination of 6 meters. what length of the pathway without lights is illuminated by the pathway with lights?

length of path illuminated = 17.615 m

Step-by-step explanation:

To solve the problem graphically,

1. draw two lines at 30 degrees to each other.

2. place lights at 0, 5, 10 from the intersection (assuming there is a light at the intersection.

3. draw circles of 6m at each light.

4. The furthest intersection of the circles with the other path is the end of the illuminated path.

5. See diagram attached, which is (6.658,5.766) from the illuminated path.

6. The distance of the un-illuminated path is obtained by Pythagoras theorem,

distance, d = sqrt(6.658^2+5.766^2) = 8.808m

Since the path is illuminated on each side of the intersection, the total length of illuminated path = 2d = 17.615m

d

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