三角形ABC中tanB为2A为π╱4求tanC的值,若a等于根号2,求边长c

Question

三角形ABC中 tanB为2 A 为π╱4 求tanC的值, 若a等于根号2,求边长c

Answer 1

tanC
=tan[π-(A+B)]
=-tan(A+B)
=-(tanA+tanB)/(1-tanAtanB)
=(tanA+tanB)/(tanAtanB-1)
=(1+2)/(2-1)
=3
tanC=sinC/cosC=3
∴C为锐角
sinC=3cosC
sin^2C =9cos^2 C=9-9sin^2 C
sinC=3√10 /10
a/sinA=c/sinC
c=asinC /sinA
=√2x3√10/10 / √2/2
=3√10 /5