Răspuns:
Explicație pas cu pas:
A=absinC/2=acsinB/2=bcsinA/2 a=BC; b=AC; c=AB=3√2
Din ultima egalitate:
acsinB=bcsinA ⇒a=bsinA /sinB si b=csinB/sinC
∡A=45°⇒ sin ∡A=√2/2 ∡C=30 sin 30°=1/2
∡B=180°-(30°+45°)=105°
sin 105°=sin (60°+45)=sin 60° cos45°+cos60°sin 45°=√3/2×√2/2+1/2×√2/2=
=√6/4+√2/4=√2/4(√3+1) ( L-am calculat suplimentar)
a=bsinA /sinB=csinB/sinC×sinA/sin B=c sin A/sin C=3√2×√2/2:1/2
=3×2=6 cm
BC=6 cm