Question

设三角形ABC的三边为a,b,c,满足tanB=2,tanC=2,b=60,则a=

Answer 1

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