[kevinkevin]

  I was looking at a SAT question and one cough my attention that I could not solve.  The question is this:  A equilateral triangle is inscribed in a circle with a radius of one.  What is the length of one of the sides of the triangle?

  The answer is the square root of three but I keep getting a different answer.  What I did was draw the triangle inside of the circle and then made a smaller triangle by using the center of the circle to draw a hypotenuse to the corner of the inscribed triangle, this hypotenuse of course has a length if one since it is also the radius.  I know know that what I was doing before was incorrect so I am assuming the reason i'm not able to solve the problem is because of a geometric property that I have forgotten.  Can anyone point me in the correct direction?
Thanks.                 

[curiouscat]

Connect centre to each vertex. 3 isoceles triangles. 120° central angles.

Drop a perpendicular on side from circle centre.

sin 60  = opp. / hyp.

hyp. = 1

Triangle side = 2 x opp.

[kevinnn]

  Thank-you. I did not think to draw all three triangles and give them central angles of 120•. That was my problem, I didn't know a way to find angle measures for my triangle I built by drawing a  Perpendicular. 

[kevinkevin]

  I thought I had it but then the math did not work.
  Square root of 3 divided by 2 is what the opposite side of 60 degrees should be.  But that answer multiplied by 2 is not the square root of three.  I'm confused again.     
 

[curiouscat]

  I thought I had it but then the math did not work.
  Square root of 3 divided by 2 is what the opposite side of 60 degrees should be.  But that answer multiplied by 2 is not the square root of three.  I'm confused again.     
 

What's the numerical value for "  Square root of 3 divided by 2". I want to check something.

[kevinkevin]

 The value is approximately 0.866 

[curiouscat]

The value is approximately 0.866

Good. Then I don't see the cause for your confusion.

[kevinkevin]

  Thats what I get for doing blind math.  But how do I achieve the square root of three.  If I was not allowed to use a calculator how would I know the correct answer since decimals were not an option?  I have not memorized the value for square root of three.     

[billnotgatez]

http://www.homeschoolmath.net/teaching/square-root-algorithm.php
How to calculate a square root without a calculator

GOOGLE and WIKI are your friends

[kevinkevin]

  Thanks.  And also my question was stupid.  If square root of three divided by two is the length of half the side then obviously the second side added to it will be square root of three. 

[curiouscat]

  Thanks.  And also my question was stupid.  If square root of three divided by two is the length of half the side then obviously the second side added to it will be square root of three.

Yes. I was expecting you were wrongly using [tex]  \sqrt \frac32  \\[/tex] instead of  [tex]\frac{\sqrt3}{2} \\[/tex]

[kevinkevin]

  Yes I was.  I have no idea why but I was.  Well now I feel stupid