Question

In triunghiul dreptunghic ABC,m(∡A)=90°,m(∡B)=60°,se stie ca BD=12 cm,unde AD⊥BC,D∈ (BC).Calculati AD si perimetrul triunghiului ABC.

Answer 1

In,tr.dr.ADB,avem,m(BAD)=30(180-90-60)=>cateta,opusa,unghiului,de,30=AB/2
BD=AB/2=>AB=24
Cu,t.Pit.aflam,AD
BDpatrat+ADpatrat=ABpatrat
144+ADpatrat=576
ADpatrat=576-144
ADpatrat=432=>AD=12radical,din,3
Cu,t.inaltimii,aflam,DC
ADpatrat=BDxDC
432=12xDC=>DC=432/12
DC=36=>BC=48
Cu,t.Pit.aflam,cateta,AC
ABpatrat+ACpatrat=BCpatrat
576+ACpatrat=2304
ACpatrat=2304-576
ACpatrat=1728=>AC=24radical,din,3
Perimetrul,tr.ABC=24+48+24radical,din,3
P=72+24radical,din,3=24(3+radical,din,3)