Question

Piramida regulata VABC are înălțimea VO=12 cm și latura bazei AB=24 cm.

URGENT,va rog!!!

Answer 1

Răspuns:

Explicație pas cu pas:

VO=12

AB=24

sin ∡(VA, (ABC))=sin ∡VAO

VO⊥(ABC)

VO⊥AO

AO⊂(ABC)

Fie AM⊥BC

$AM=\frac{l\sqrt{3} }{2} =12\sqrt{3}$

$AO=\frac{2}{3} \cdot 12\sqrt{3} =8\sqrt{3}\\ OM=4\sqrt{3}$

In ΔVAO aplicam pitagora

VA²=AO²+VO²

VA²=192+144=336

VA=4√21

sin∡VAO=$\frac{VO}{VA} =\frac{12}{4\sqrt{21} } =\frac{\sqrt{21} }{7}$

Fie AN⊥VM ⇒ d(A,(VBC))=AN

VM⊂(VBC)

In ΔVOM pitagora

VM²=VO²+OM²

VM²=144+48=192

VM=8√3

aplicam aria in 2 moduri in ΔVAM

$\frac{VO\cdot AM}{2}=\frac{AN\cdot VM}{2}$

12×12√3=AN×8√3

AN=18 cm

∡((VBC),(ABC))=∡VMA

VM⊥BC, VM⊂(VBC)

AM⊥BC, AM⊂(ABC)

tg∡VMA=tg∡VMO=$\frac{VO}{OM} =\frac{12}{4\sqrt{3} } =\sqrt{3}$