Answer:
For a 30-60-90 right triangle, the side opposite the 30 deg angle is always 1/2 the hypotenuse.
Suppose the sides are 30-A, 60-B, and 90-C where A, B, and C are opposite the angles
Then the side opposite the 60 deg angle is (C^2 - A^2)^1/2 = B
A simple example is A = 1, C = 2, and B = (2^2 - 1^2)^1.2 = 3^1/2 /2
So the simplest triangle is 1, .866, 2
Take #4 as an example where b = 1 * 1/2 * 72 = 36
In #1 you have 6 * 3^1/2 / a = 3^1/2 / 2 or a = 3
Just note A / B = 1 / (3^1/2) = 1.732 / 3 = .577 (Also 1 / 2 = tan 30 deg
A / C = 1 / 2 = .5 B / C = 3^1/2 / 2 = .866
Just know the sides are 1 , 3^12 , 2 or 1^2 + 3 = 4 that is A^2 + B^2 = C^2