Question

50 PUNCTE!
Fie trapezul isoscel ABCD , BCIIAD, AC⊥CD, m(<D)=60 grade. AD=12cm. De aflat AB,BC,AC

Answer 1

tr. ACD e dreptunghic in C si cu ∡D=60°, rezulta ∡CAD=30° si cu T∡30° avem:
CD=AB=AD/2=6
ducem:
BE⊥AD, E∈AD
CF⊥AD, F∈AD
observam ca:
∡ABE=∡FCD=30° ⇒ T∡30° ⇒ AE=FD=AB/2=CD/2
AE=FD=3
BC=AD-AE-FD=12-3-3
BC=6
cu pitagora in tr. ACD rezulta AC
AC=√(AD^2-CD^2)=√(12^2 - 6^2)
AC=6√3