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Here's another solution...
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Posted by zeke (more from zeke) on Sat, 20 Nov 2004 17:28:54 Share Post by Email
In Reply to: if you passed high school geometry read on..., Liam, Thu, 18 Nov 2004 12:56:10
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Like GeneN's, it also involve the use of any auxilliary lines and does use trig': the law of cosines, which states the square of the side of any triangle equals the sum of the squares of the other two sides minus the product of the other two sides multiplied by the cosine of their included angle. In this case, the included angle would be 120º and the two sides would each measure 10. The cosine of 120º, because it's in the 2nd quadrant, is the negative of the cosine of 60º, ie., -1/2.
The sum of the square of both sides (10) is 200. Twice the product of both sides is 200 but multiplied by -1/2 gives -100. However, we're subtracting a negative, so adding 100 to 200 gives 300, which is the square of the side we're looking for - another way of expressing the answer would be to say that the side of the triangle measures the square root of 300.

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