Question

In triunghiul ABC cu m(A)=90grade ,construim inaltimea AD,De(BC) ,Daca :
a)tgB=1,5 si CD=10cm ,aflati BD
b)ctg C =1,2 si BD =5cm ,aflati CD

Answer 1

a) tgB = AC/AB = 1,5
ΔADC asemenea  ΔABD   (∡DAC ≡∡B, AD latura comuna)
AC/AB = DC/AD = AD/BD = 1,5
AD = DC/1,5    AD = 1,5BD  ⇒⇒ DC/1,5 = 1,5BD ⇒⇒
⇒⇒ BD = DC/2,25 = 10/2,25 = 1000/225 = 40/9 cm
b) AB/AC = 1,2
ΔABD asemeneaΔACD  (∡B =  ∡DAC)
AB/AC = BD/AD = AD/DC = 1,2
AD = BD/1,2 = 1,2DC    ⇒  CD = BD/1,44 = 5/1,44 = 500/144 = 125/36 cm