I have deduced an equation of a right triangle using the trigonometric ratio sine can i apply that equation for example to the moon and two stars to determine the distance from one another?
I think not, as the stars are not in the same plane. One of the two could be actually closer to the earth than the other, so what you might end up is the arc distance between those two. I m not sure, but this is my understanding. If you could actually, it would be great :). Try the formula for alpha centauri and sirius. That might help if u get the distance between the two correctly using your formula and the actual distance between the two.