设三角形ABC的三边为a,b,c,满足tanB=2,tanC=2,b=60,则a=
问题描述:
设三角形ABC的三边为a,b,c,满足tanB=2,tanC=2,b=60,则a=
答
tanB=2,tanC=2 ∠B=∠C
tanB=2
sinB=2cosB
sin²B=4cos²B
sin²B=4-4sin²B
sin²B=4/5
sinB=2√5/5
cosB=√5/5
sinA=sin(B+C)=sin2B=2sinBcosB=2*2√5/5*√5/5=4/5
a/sinA=b/sinB
a=60/2√5/5 *4/5=120/√5=24√5