Can anyone help me with 30-60-90 special right triangles?

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

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step-by-step explanation: