Question

In triunghiul DEF m(DEF)=90 de grade tg(EDF)=3 supra 4 si DF=10.Sa se afle lungimile catetelor EF si DE.

Answer 1

tg(D)=3/4
sinD/cosD=3/4  ridicam la patrat
sin^2(D)/cos^2(D)=9/16
aplic propietatile proportiilor
sin^2(D)/[cos^2(D)+sin^2(D)=9/(16+9)
sin^2(D)=9/25
sin(D)=3/5
dar sin(D)=EF/FD  deci 3/5=EF/10 deci EF=6
aplic Pitagora sa aflu cealalta cateta
DE^2=DF^2-FE^2=100-36=64
DE=8