Question

已知a,b,c是△ABC的三边,S是△ABC的面积,若a=4,b=5,S=5√3,则边c的值为____________.

Answer 1

S=5√3=1/2*a*b*sinC

sinC=√3/2

所以cosC=1/2或-1/2

当cosC=1/2时,c^2=a^2+b^2-2abcosC=16+25-20=21

c=√21

当cosC=-1/2时,c^2=a^2+b^2-2abcosC=16+25+20=61

c=√61