在三角形ABC中，c+b=2a，3sinA=5sinB，求角C(2013安徽高考数学题)

简便方法

c+b =2a, 经正弦定理转化，　即

sinC + sin B = 2 sinA

sinB = 3/5 sinA 代入

sinC = 2 sinA - 3/5 sinA = 7/5 sinA

所以

sinC/ 7 = sinA/5

sinA/5 = sinB /3

a = 5k, b=3k, c=7k

cosC = (b? +a? -c?)/2ab = (9 + 25 - 49)/2*5*3= -1/2

C = 120°