Out of Pod Experience

Triangle1: S^2 + L^2 = H^2

Triangle2: s^2 + l^2 = h^2

We know: s^2 = S^2 and h^2 = H^2

from this we get: L^2 = H^2 - S^2 for Triangle 1 and l^2 = h^2 - s^2 for triangle 2


knowing that both the hypotenuse AND the shortest side are equal on both triangles we can say that the hypotenuse minus the short side on both triangles is ALSO equal

So, our equation looks like this


L^2 = H^2 - S^2 = h^2 - s^2 = l^2

Therefore: L^2 = l^2 You have equal triangles and therefore the angle between the shortest side and the hypotenuse will be the same on both triangles.

In case you want to "learn" something: Math Is Fun!

I am with Akita T. Make sure those are right triangle. Since you say one side is hypotenuse, then we assume it is right triangle. Since it is right triangle, we can use the Pythagorean Theorem, that Calico-Jack Daniels explained, to find the third side of both triangles. This will give you the proof that the two triangles are identical. You use the fact that two triangles are identical as proof that specific elements of each triangle are identical.

If I remember my geometry right, there are several ways to prove that two triangles are identical:
1) Show that two triangles have identical length sides. Say Triangle 1 has sides A, B, C. Triangle 2 has sides x, y, z. If you can show that A=x, B=y, C=z, then Triangle 1 = Triangle 2. Which in turn means that all the angles in Triangle 1 equal to corresponding angles in Triangle 2.
2) Show that all the angles in one triangle are equal to corresponding angles in second triangle.
3) Show that two sides and angle between them in one triangle are equal to corresponding two sides and angle in second triangle.


I have an ugly feeling that your triangles are not actually right triangles. In this case you can not use Pythagorean Theorem. However, there there are two laws that are very useful in this case, Law of Sines, Law of Cosines. Since you know two sides and one angle of each triangle, you can use the two laws to find all the missing pieces. The beauty of these laws is that they work on any triangle.
Law of Sines: https://classroom.peoriaud.k12.az.us/sites/caylward/Classroom%20Images/Precal%20Sem%202/Trenton%20Flores/formula-picture-law-of-sines.gif
Law of Cosines: http://www.mathwarehouse.com/trigonometry/images/law-of-cosines/law-of-cosines-formula-and-picture2.gif

P.S.: It sounds like you only need Law of Sines.

You know the matari dudes, we don't care about stupid wands, all we care is the triangulation of our UZIs.

For engaging multiple targets.
http://www.youtube.com/watch?v=uaJPd5qyW5I