Răspuns:
Explicație pas cu pas:
tg(C)=AB/AC => AB=AC*tg(C)
AB=6*0.5=3cm
Aria = AB*AC/2 = 3*6/2=9 cm²
sin(C) = AB/BC
cos(C)=AC/BC
sin²(C)+cos²(C)=(AB/BC)²+(AC/BC)²=AB²/BC² + AC²/BC² = (AB² + AC²)/BC² = (t. Pitagora) = BC²/BC²=1
BC=√(AB²+AC²)=√(9+36)=√45=3√5 cm
Atunci AD = AB*AC=BC=3*6/3√5=6/√5=6*√5/5
iar CD = √(AC²-AD²)=√(36-36/5)=√144/5=12/√5=12*√5/5
sin(DAC)=CD-AC=(12*√5/5)/6=2*√5/5
cos(DAC)=AD/CA=(6*√5/5)/6=√5/5