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Here's another solution...
Posted by zeke (more from zeke) on Sat, 20 Nov 2004 17:28:54
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.
posted by 24.91.254...
Posts in this Thread:
- if you passed high school geometry read on..., Liam, Thu, 18 Nov 2004 12:56:10
- Here's another solution..., zeke, Sat, 20 Nov 2004 17:28:54 <-- Viewing This Message
- So, the question remains....>>>, PGAero , Thu, 18 Nov 2004 16:34:40
- Re: if you passed high school geometry read on..., Liam, Thu, 18 Nov 2004 16:11:03
- 10" x (the square root of 3), or ~17.32", IrieTom , Thu, 18 Nov 2004 13:37:03
- Re: if you passed high school geometry read on..., Gene N , Thu, 18 Nov 2004 13:35:29
- There's only one equilateral triangle that can be..., zeke, Thu, 18 Nov 2004 13:35:00
- Re: square that diameter and 1/2? n/m, t_mokes, Thu, 18 Nov 2004 13:11:35
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