octoberchick1011
An equilateral triangle with sides of length 6 is inscribed in a circle. What is the diameter of the circle?



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dpaInc
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dw:1337641995914:dw
because your dealing with a 306090 triangle, you can solve that triangle for r:
3^2 = (3/2)^2 + r^2
solve for r, your radius.

octoberchick1011
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Okay! Thank you! :)

dpaInc
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yw... you want an answer verification?

octoberchick1011
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Yes please!

dpaInc
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ok.. tell me what u got an i'll tell you mine...

octoberchick1011
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Well, for the answer to the question, I got 6.9.. Is that right?

dpaInc
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i got 3(sqrt3)/2 or about 2.6

dpaInc
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hmm... wanna go over the work?

asnaseer
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6.9 is the correct answer for the diameter

dpaInc
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ohh... hahah... thanks @asnaseer ..

asnaseer
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yw :)

dpaInc
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sorry, I meant @octoberchick , your correct... :)

asnaseer
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btw: I did it in a slightly different way:
dw:1337643034380:dw
bisect one of the angles of the equilateral triangle to get...

asnaseer
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dw:1337643091539:dw

asnaseer
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then, in the right angled triangle ABC:\[\cos(30)=6/d\]therefore:\[d=6/\cos(30)\]

dpaInc
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wow....
isn't it great having to see other methods? and this is still a 306090 triangle so trig functions aren't really needed still.
thanks... :)

asnaseer
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true... :)

dpaInc
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and i think that is a lot more clear ^^^... :)