Răspuns:
a)P△ ABC=60cm
b)A△ADB=96cm²
c)sin(∢BAD)=4/5
cos(∢BAD)=3/5
tg(∢CAD)=3/4
Explicație pas cu pas:
△ ABC; ∢A=90°;AD perpendicular pe BC;AD=12cm; cosC=3/5
a) AC/BC=3/5; AC=3k; BC=5k
AB²=BC²-AC²=25k²-9k²=16k²
AB=4k
AB*AC=BC*AD
4k*3k=5k*12cm
12k²=60k
k=5
=> AB=4*5=20cm; AC=3*5=15cm; BC=5*5=25cm
P△ ABC=AB+AC+BC=20cm+15cm+25cm=60cm
b) BD²=AB²-AD²=400cm²-144cm²=256cm²
BD=16cm
A△ ADB=BD*AD/2=16cm*12cm/2=96cm²
c)
în △ BAD:
sin(∢BAD)=BD/AB=16cm/20cm=4/5
cos(∢BAD)=AD/AB=12cm/20cm=3/5
CD=BC-BD=25cm-16cm=9cm
în △ CAD:
tg(∢CAD)=CD/AD=9cm/12cm=3/4
