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30 60 90 Triangle

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Jinglander » Sat Aug 14, 2010 5:49 pm
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
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by Brent@GMATPrepNow » Sun Aug 15, 2010 6:45 am
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

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by Jinglander » Sun Aug 15, 2010 9:00 am
Can some other triangle (perhaps not right) have these sides with different angles
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by Brent@GMATPrepNow » Sun Aug 15, 2010 4:52 pm
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.
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