在三角形ABC中,若三内角满足sin^A=sin^B+sinB乘sinC+sin^C,则角A等于?
问题描述:
在三角形ABC中,若三内角满足sin^A=sin^B+sinB乘sinC+sin^C,则角A等于?
A 30°
B 60°
C 120°
D 150°
答
应该是(sinA)^2=(sinB)^2+sinB*sinC+(sinC)^2
设三角形外接圆半径为R则
(2RsinA)^2=(2RsinB)^2+2RsinB*2R*sinC+(2RsinC)^2
=>a^2=b^2+bc+c^2=>b^2+c^2-a^2=bc=>cosA=(b^2+c^2-a^2)/2bc=1/2=>A=60