30 60 90 Triangle

Jinglander wrote:I know that if you know a tirangle is a 30 60 90 and you know one side you can solve for all. What about if you know all the sides are in the formation of the 30 60 90 ie x, x sqrt(3) and 2x and I know one of the angles is 90 can I be assured it is a 30 60 90

This is more information than you need (you don't need the 90-degree angle).

If you know that the lengths of the 3 sides are in the ratio x : xroot3 : 2x, then you are guaranteed a 30-60-90 triangle.
The angle opposite the longest side (2x) will be 90 degrees
The angle opposite the shortest side (x) will be 30 degrees
And the last angle will be 60 degrees

Brent

Jinglander wrote:Can some other triangle (perhaps not right) have these sides with different angles

If you know the lengths of all 3 sides, there is only 1 triangle possible.
Try it out. Take 3 pens/sticks/etc with various lengths and see how many different triangles you can create.

So, if the lengths of the 3 sides have the ratio x : xroot3 : 2x, then you must have a 30-60-90 triangle.