Question

在△ABC中,c=2倍根号2,tanA=3,tanB=2则s△ABC是多少

Answer 1

tanc=-tan(a+b)

=-(tana+tanb)/(1-tanatanb)

=1

c=45°,sinc=√2/2.

sina=3/√10,

sinb=2/√5,

a=csina/sinc=(2√2)*(3/√10)/(√2/2)=6√10/5

b=csinb/sinc=(2√2)*(2/√5)/(√2/2)=8√5/5

面积S=1/2absinC=24/5.