Question

Fie triunghiul abc cu m(a)=90 ab _|_ bc D apartine (BC) D=9 cm si tg C =2/3 a)Calculati lungimile laturilor triunghiului b)Calculati sin b si cos b

Answer 1

in triunghiul ACD: tg C=AD/DC adica AD=DC*2/3=9*2/3=6cm 
teorema inaltimii in ACB spune ca
AD^2=CD*DB deci DB=AD^2/CD=6*6/9=4cm
deci BC=CD+DB=9+4=13cm
cu teorema catetei in ACB
AB^2=BD*BC=4*13=52
AB=2rad13
tgC=AB/AC deci AC=AB/tgC=2rad13/(2/3)=3rad13
cosB=DB/AB=4/2rad13=2rad13/13
sinB=AD/AB=6/2rad13=3rad13/13