Răspuns:
Explicație pas cu pas:
ΔBDA sin ∡(BAD)=3/5 =DB/AB⇒AB=DB/sin ∡(BAD)=9/(3/5)=(9·5)/3=15cm
AB=15 cm
Δ DAB T.Pitogara AD²=AB²-DB²=225-81=144⇒AD=12 cm;
Δdr BAC m∡(A)=90° T.inaltimii AD²=DC·DB⇒DC=AD²/DB=144/9=16 cm
DC=16 cm; BC=DC+DB=16+9=25 cm; BC=25 cm;
ΔBAC T.Pitagora AC²=BC²-AC²=625-225=400⇒AC=20 cm;
Perimetru ΔABC=25+15+20=60 cm;
Aria ΔADC=AD·DC/2=16·12/2=96 cm²
