Question

Să se calculeze aria triunghiului ABCin cazul b=9, A=pi/3, C=(5pi)/12

Answer 1

Daca m(<A)=π/3, in grade ar fi m(<A)=60°.
Daca m(<C)=5π/12, in grade ar fi m(<C)=5*180/12=75°.
Putem afla si m(<B):
m(<B)=180°-(m(<A)+m(<B))=180°-(60°+75°)=180°-135°=45°
Aplicam teorema sinusului:
b/sinB=a/sinA
9/sin45°=a/sin60°
9/√2/2=a/√3/2
18/√2=2a/√3
2a√2=18√3
a=18√3/2√2=9√3/√2=9√6/2
sinC=sin(30°+45°)=sin30°cos45°+cos30°sin45°=√3*√2/4+1*√2/4=(√6+√2)/4
A=a*b*sinC/2=9√6*1/2*9*(√6+√2)/4=81√6(√6+√2)/8=(486+81√12)/8=(486+162√3)/8=60.75+20.25√3