You get close, but not exact, with a triangle that has sides 20, 19, and 16. The height (with 19 as the base) is 14.9462. There are four different triangles you can form with three of the chopsticks. Each of the triangles has three heights since there are three choices for a base. Here are the numbers for 15, 16, 19, 20:
Code:
Sides Heights (ordered to match bases)
20 19 16 14.1989 14.9462 17.7487
20 19 15 13.4700 14.1789 17.9600
20 16 15 11.8279 14.7849 15.7705
19 16 15 12.2305 14.5237 15.4919
Here's a useful formula for the area of a triangle given sides of length A, B, C:
S = (A+B+C)/2 (semi-perimeter)
Area = sqrt(S * (S-A) * (S-B) * (S-C))
To calculate the three heights of a triangle, calculate the area, and multiply it by 2 (area*2). Then, for each side (base), divide the area*2 by the length of the side. That is the height.