Question

已知三角形abc周长为根号三加一,面积为3/8乘C的正弦值,且A的正弦值加B的正弦值等于根号三C

Answer 1

a+b+c=1+√3,S=3/8sinC,sinA+sinB=√3sinC

S=1/2absinC=3/8sinC

ab=3/4

a+b=√3c,a+b+c=1+√3

c=1,a=b=√3/2

cosC=(a^2+b^2-c^2)/2ab=(3/2-1)/3/2=1/3

sinC=2√2/3

tanC=2√2

tan(A+B)=-tanC=-2√2