Question

    ABC的内角A、B、C的对边分别为a、b、c，已知a=，b=，B=45^o，

(I)求角A、C；

(Ⅱ)求边c．

Answer 1

解  (Ⅰ)∵B=45°＜90°且asinB＜b＜a,∴△ABC有两解.

由正弦定理得sinA== =,

则A为60°或120°.                                 

                                                                                                                                                   

（Ⅱ）①当A=60°时，C=180°-(A+B)=75°,

c====.          

②当A=120°时，C=180°-(A+B)=15°,

c====.             

故在△ABC中，A=60°,C=75°,c=或A=120°,C=15°,c=.