Question

(1/2)已知三角形ABC的周长为根号2+1,且sinA+sinB=根号2sinC,1.求边c的长.2.三角形ABC的面

Answer 1

a/sinA=b/sinB=c/sinC=k

sinA+sinB=√2sinC

a+b=√2c

a+b+c=√2+1

c=1

a+b=√2

S=(1/2)absinC=(1/6)sinC

ab=1/3

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

C=60