Question

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Answer 1

Explicație pas cu pas:

A=(AB+CD)*AD/2=(100+60)*40√3/2=160*20√3=3200√3 (m²)

m(<A)=m(<D)=90°

Ducem inaltimea CK

CK⊥AB

AB=AE+EK=DC

AE+EK=60

AB=AE+EK+EK

100=60+EK⇒KB=EK=40(m)

tg(<C/2)=KB/CK

tg(<C/2)=40/40√3=√3/3

arctg√3/3=m(<C)/2⇒m(<C)=2*arctg√3/3⇒m(<C)=2*30°⇒m(<BCD)=60°

m(<E)=m(<B)

In triunghiul CBE;

2*m(<E)+m(<C)=180°

m(<E)=m(<B)=(180°-m(<C)/2⇒m(<E)=m(<B)=(180°-60°)/2=120°/2=60°

m(<E)=m(<C)=m(<B)=60° demonstreaza ca ΔCEB este echilateral

Bafta!