Question

In triunghiul ABC se cunosc AB=17 CM , AC= 10 cm , BC=21 cm. Aflati aria triunghiului , sin (

Answer 1

Calculam Aria cu formula lui Heron:
p=(17+10+21)/2=48/2=24
A=√(p(p-a)(p-b)(p-c))=>
A=√24×(24-17)(24-10)(24-21)=>
A=√(24×6×14×3)=>
A=√(2×2×2×3×2×7×3)=>
A=4×3√7=>
A=12√7 (cm^2)
A=(AC×BC×sin(C))/2=>12√7×2=10×21×sin(C)=>
sin(C)=(24√7)/210=>
sin(C)=(12√7)/105
Fie AE perpendicular pe BC, E apartine BC
A=(BC×AE)/2=>
AE=(A×2)/BC=>
AE=(24√7)/21=>
AE=(8√7)/7
Sper ca am fost de ajutor!