Question

Aflati aria triunghiului ABC in fiecare dintre situatiile :
a)AB= 3√2 cm, BC=4 cm si m( b) AC= 10 dm, BC=15 dm si m ( c) AC= 5 cm, AB= 7m si sin A =0.6;
d) AB= 10√3 dm, m (<ABC)= 60 de grade si BC=16 dm. 

Answer 1

a)AB= 3√2 cm, BC=4 cm si m(abc)=45 ⁰
AD inaltime
sin 45⁰=AD/AB
√2/2=AD/3√2
AD=√2/2 x3√2 = 3
A=ADxBC/2=3x4/2=6 cm²

b) AC= 10 dm, BC=15 dm si m (acb)=30⁰
sin 30⁰=AD/AC
1/2=AD/10
AD=1/2 x10= 5
A=ADxBC/2=5x15/2=37,5 dm²

c.AC= 5 cm, AB= 7cm si sin A =0.6;     
BD inaltime
sin A=BD/AB
0,6=BD/7
BD=4,2
A=ACxBD/2=5x4,2/2=10,5 cm²

d) AB= 10√3 dm, m (<ABC)= 60⁰ si BC=16 dm.
AD inaltime
sin 60⁰=AD/AB
√3/2=AD/10√3
AD=√3/2 x10√3 = 15
A=ADxBC/2=15x16/2=120 dm²