Question

Sa se calculeze aria triunghiului ABCin cazul a=6, C=pi/3, A=pi/4

Answer 1

Aplicam teorema sinusului:
a/sin A=c/sin C
6/sin π/4=c/sinπ/3
6/sin 45°=c/sin60°
6/√2/2=c/√3/2
12/√2=2c/√3
2c√2=12√3
c=12√3/2√2=6√3/√2=6√6/2=3√6
A=a*c*sinB/2=6*3√6*sinB/2=9√6*sin B
m(<B)=180°-45°-60°=75°
sinB=sin(30°+45°)=sin30°cos45°+cos30°sin45°=√3*√2/4+1*√2/4=(√6+√2)/4
A=9√6*(√6+√2)/4=(54+9√12)/4=(54+18√3)/4