sinB/sinA =10/9(下证), 面积为1/2 a c sin B= 1/2 R c sinB/sinA = 5/9 c^2/sin C
c已知,sin C =2根号2 /3 易得.
设 x=sin B/sinA.
首先要计算 sin^2 C =8/9, cos C =1/3
由2sin B =sin A +sin C 可得 2x =1+ sin C/ sin A (1)
再利用 B= 180-A-B得
x =(sin Acos C +cos A sin C)/sin A = 1/3 + sin C cos A/sin A (2)
利用两式消掉A 得
(2x-1)^2 *9/8 = (x-1/3)^2 *9/8 +1,
解方程得 x=10/9, 或 0(舍弃)