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.
To solve this problem, we'll break it down into steps.
Step 1: Determine the length that is effectively illuminated by each light.
The effective illumination range of each light is 6m. This means that any point within 6m of a light will be effectively illuminated.
Step 2: Calculate the distances between lights.
The distance between successive lights is 5m.
a.) To find the length that is effectively illuminated by the second light, we need to determine the point at which the effective illumination of the first light ends and the second light begins.
Since the distance between the lights is 5m, and the effective illumination range of each light is 6m, there will be an overlap of 1m. Thus, the second light will start illuminating 1m before the end of the first light's effective range. Therefore, the length effectively illuminated by the second light is 6m - 1m = 5m.
b.) To find the length that is effectively illuminated by both the second and third light, we need to determine the point where the effective illumination of the second light ends and the third light begins.
Similarly to the previous step, there will be an overlap of 1m between the second and third lights. So the length effectively illuminated by both the second and third light is 6m - 1m = 5m.
c.) To find the length that is effectively illuminated by the third or fourth light, we need to determine the portion where the effective illumination of the third light ends and the fourth light begins.
Again, there will be an overlap of 1m between the third and fourth lights. So the length effectively illuminated by the third or fourth light is 6m - 1m = 5m.
Therefore, to the nearest tenth of a metre:
a.) The length effectively illuminated by the second light is 5m.
b.) The length effectively illuminated by both the second and third lights is 5m.
c.) The length effectively illuminated by the third or fourth light is 5m.