Question

Calculati aria si perimetrul unui triunghi Abc in care se cunoaste m(<A)=75 grade
m(<B)=45 grade
AC=12 radical din 3cm

Answer 1

Δ ADBm(<BAD)=45°   deoarece triunghiul este dreptunghic cu un unghi de 45°rezulta BD=AD =a2a²=(12√6)²2a²=864a²=432a=12√3   AD=12√3
m(<DAB)=75°-45°=30°m(<ACB)=90°-30°=60°sin 30°=1/2AD/AC=12√3/AC=1/2       AC=12√3 ×2=24√3DC=√(AC²-AD²)=√[(24√3)²-(12√3)²]=√(1728-432)=√1296=36BC=12√3+36
ΔΔBECsin 60° =√3/2BE/BC=BE/(36+12√3) =√3/2 BE=(36+12√3) ×√3/2=(36√3+36) /2=18+18
PABC=12√6+24√3+12√3+36=12√6+36√3+36=12(√6+3√3+3)

Answer 2

ducem AD⊥BC si cu notatiile din figura avem:
tr. dr. ABD are ∡B=45° ⇒ tr. ABD este isoscel ⇒ AD=BD=x cm, AB=x√2 cm
T∡30° in ACD ⇒ DC=AC/2=6√3 cm
x=18 cm (vezi pitagora in ACD)
AB=18√2 cm
BC=BD+DC=18+6√3 cm
perimetrul
P=AB+AC+BC=18√2+12√3+18+6√3
P=18(1+√2+√3) cm
aria ABC
A=BC x AD/2=(18+6√3) x 18/2
A=54(3+√3) cm2