Originally posted by oscar at 2005-3-30 07:58 PM: 有時做數就是那麼無奈.... 我都試過........ http://www.xanga.com/home.aspx?user=LWrabbit Wednesday, March 23, 2005 Question
In triangle ABC, let a/sinA=b/sinB=c/sinC=k,where A,B and C are interior angles. (a)show that a/sinA=a+b+c/sinA+sinB+sinC (b)略 (c)略 my answer
i divide it into two part...... ======================= a+b+c=k(sinA+sinB+sinC) ======================= sinA+sinB+sinC=(a+b+c)/2 ======================= therefore a+b+c / sinA+sinB+sinC =k^2(sinA+sinB+sinC) / k(sinA+sinB+sinC) =k therefore = a /sin A answer
a+b+c / sinA+sinB+sinC = k(sinA+sinB+sinC) / sinA+sinB+sinC = k = sin A ................. [ Last edited by smallpotato226 on 2005-3-30 at 08:07 PM ] |