Question

In triunghiul ABC, ascutitunghic,AD este inaltime,AD=36 cm, sin (B)=12/13 si cos (C)=3/5.Aflati aria triunghiului.

Answer 1

sin B=12/13=AD/AB
12/13=36/AB
AB=(36x13)/12=39 cm
BD=√(39²-36²)=√(1521-1296)=√225=15 cm

cos C=3/5
sin C =√1-cos² C=√[1-(3/5)²]=√(1-9/25)=√(25-9)/25=√16/25=4/5
sin C=AD/AC
4/5=36/AC
AC=36x5/4=45 cm

cos C=3/5
3/5=DC/45
DC=45x3/5=27 cm
BC=BD+DC=15+27=42 cm

Aria triunghiului=42x36/2=756 cm²