In triangle ABC,angle ABC=60 degree.
O is a point inside triangle ABC such that
angle AOB= angle AOC= angle BOC
If AO=3 and CO=4,find the length of BO.
Problem about triangle
2008-06-19 1:05 am
回答 (1)
2008-06-19 1:57 am
✔ 最佳答案
(a)Let angle OBA = x, angle CBA = y. Therefore x + y = 60 (given) or x = 60 - y ...(1)(b) Let OB = m. For triangle AOB, by sine rule, m/sin(60 - x) = 3/sinx because angle BOA = 120. Or m/sin(60- x) = 3/sin(60- y).....................(2)
(c) For triangle COB, by sine rule, m/sin(60-y) = 4/siny or m/sin(60-y) = 4/sin(60-x)............(3)
(d) (2) x (3), we get m^2/[sin(60-x)(sin(60-y)] = 12/[sin(60-y)sin(60-x)],
therefore, m^2 = 12, therefore, m = BO = sqrt12.
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