题目

1.已知△ABC中,∠A=π/3,a=10求三角形周长的最大值

提问时间：2021-03-20

答案

正弦定理：sina/a=sinb/b=sinc/c
b=20sinb/根号下3 c=20sinc/根号下3
a+b+c=10+20(sinb+sinc)/根号下3
=10+20[sin(120-c)+sinc]/根号下3
=10+20[根号下3cosc/2+sinc/2+sinc]/根号下3
=10+20(根号下3cosc/2+3sinc/2)/根号下3
=10+20根号下3sin(c+π/3)/根号下3
=10+20sin(c+π/3)
π/3