设AC=aBC=b 作CD垂直AB　,ME垂直AB
CM=BM=b/2
AM=根号(a^2+b^2/4)
CD=2ME
sinBAM=ME/AM =1/3ME=AM/3
CD=ab/根号(a^2+b^2)
1/2ab/根号(a^2+b^2)=根号(a^2+b^2/4) /3
9a^2b^2=4(a^2+b^2)(a^2+b^2/4)
9a^2b^2=(a^2+b^2)(4a^2+b^2)=4a^4+5a^2b^2+b^4
4a^4-4a^2b^2+b^4=0
(2a^2-b^2)^2=0
2a^2=b^2
所以sinBAC=CD/AC=ab/a根号(a^2+b^2) =b/根号(a^2+b^2)=根号6 /3