" Pink Floyd rocks"
I can only agree with this statement, in both senses of the word...

A way to do it is to express the anchor points of the lines in ratio/percentage of the length of the line representing the side.
Ie. the first ray of light starts at 0.25 * lineLength (approximative), the last one at 0.5, the others in proportional ratios.

Then, given the equation of a line in 2D space, it is easy to compute the location of these starting points according to the dimension & position of the line.

Well, my answer can apply as well on the left side...
Either you show your code, so we can suggest improvements, or you keep getting general advices, hopefully clear enough to allow you to implement the feature.

Ouch, everything is hard-coded! Impressive work, but it means hard-to-animate...

We have y = a.x + b
aX, aY are the anchor points of the moving line (bottom left of the triangle) -- 500, 440
tX, tY are the top triangle corner coordinates -- 640, 180
aY = a.aX + b
tY = a.tY + b
aY - tY = a.(aX - tX) => a = (aY - tY) / (aX - tX) = -1.857
So b = aY - a.aX = 1654.286

Beam line joins at 581, 290, which is confirmed by the equation above: 1368.5-1.857*581 = 289.58
Total length: sqrt((640-500)^2 + (180-440)^2) = 295
Length to join point: sqrt((581-500)^2 + (290-440)^2) = 170
Ratio = 0.577

Mmm, perhaps I have made things harder than it needed...
Anyway, here is a change of your code to keep the beam on the moving triangle:

1. //Dark Side of the Moon Album Cover
2. void setup() {
3.   size(1280, 720);
4.   smooth();
5. }
6. 
   
7. int anchorX = 500, anchorY = 440;
8. float a = -1.857, b = 1654.286;
9. float r = 0.577;
10. int tX = 640, tY = 180;
11. 
    
12. void draw() {
13.   background(0);
14. 
    
15.   //outer triangle
16.   noStroke();
17.   fill(194, 250, 247);
18. //  triangle(tX, tY, anchorX, anchorY, 780, 440);
19.   triangle(mouseX, mouseY, anchorX, anchorY, 780, 440);
20. 
    
21.   //inner triangle
22.   noStroke();
23.   fill(0);
24.   triangle(640, 200, 520, 430, 760, 430);
25. 
    
26.   //alpha triangle
27.   noFill();
28.   stroke(142, 247, 241, 191);
29.   strokeWeight(10);
30.   triangle(640, 200, 520, 430, 760, 430);
31. 
    
32.   //light beam
33.   float ix = anchorX + r * (mouseX - anchorX);
34.   float iy = anchorY + r * (mouseY - anchorY);
35.   stroke(255);
36.   strokeWeight(2);
37. //  line(0, 400, 581, 290);
38. //  fill(#FF0000); noStroke(); ellipse(581, 290, 2, 2);
39.   line(0, 400, ix, iy);
40.   fill(#FF0000); noStroke(); ellipse(ix, iy, 2, 2); // Debug: visually check the join point
    
41. 
    
42.   //light beam array (beginning)
43.   noStroke();
44.   fill(245, 245, 245, 191);
45.   triangle(579, 290, 640, 270, 640, 300);
46. 
    
47.   //light beam array (end)
48.   noStroke();
49.   fill(245, 245, 245, 120);
50.   quad(640, 270, 682, 259, 710, 310, 640, 300); 
51. 
    
52.   //rainbow
53.   //purple ray
54.   noStroke();
55.   fill(167, 110, 188);
56.   quad(705, 300, 1280, 400, 1280, 420, 710, 310);
57. 
    
58.   //blue ray
59.   fill(79, 196, 252);
60.   quad(700, 290, 1280, 380, 1280, 400, 705, 300);
61. 
    
62.   //green ray
63.   fill(119, 198, 86);
64.   quad(696, 283, 1280, 360, 1280, 380, 700, 290);
65. 
    
66.   //yellow ray
67.   fill(254, 255, 18);
68.   quad(692, 275, 1280, 340, 1280, 360, 696, 283);
69. 
    
70.   //orange ray
71.   fill(232, 160, 14);
72.   quad(688, 268, 1280, 320, 1280, 340, 692, 275);
73. 
    
74.   //red ray
75.   fill(255, 9, 0);
76.   quad(683, 259, 1280, 300, 1280, 320, 688, 268);
77. }