Question

Vă rog , acest exercițiu (3) !!!

Pas cu pas !!!

Answer 1

Răspuns:

Explicație pas cu pas:

In ΔABC  ducem AD⊥BC

in Δdreptunghic ABD   cu ∡B=60°   ctg B=BD/AD=√33     BD=√3/3AD

in Δ dreptunghic  ADC  ctg∡C=DC/AD   DC=ADctg 75°

ctg C=ctg 75°=ctg(30°+45°)=(ctg30°ctg45°-1)/ctg30°+ctg45

ctg 30°=√3     ctg 45°=1

ctg 75°=(√3-1)/(√3+1)=(√3-1)(√3-1)/(3-1)=(3-2√3+1)/2=2(2-√3)/2=2-√3

BC=BD+DC=AD√3/3+AD(2-√3) =AD(√3+6-3√3)=AD(6-2√3)=2AD(3-√3)

AD=BC/2(3-√3)=BC(3+√3)/2(9-3)=BC(3+√3)/12

A=ADxBC/2=BC(3+√3)/12×BC/2=BC²(3+√3)/24

A=12²(3+√3)/12x2=6(3+√3) cm²