Question

I.)ABCDA'B'C'D' este paralelipiped dreptunghic
Ac=a
m(AB,AC)=30°
m((BD'(ABC))=45°
C.)L,l,h=?

Answer 1

inΔABC BC=AC/2=a/2-latimea
AB²=AC²-BC²
AB²=a²-a²/4=3a²/4
AB=a√3/2=lungimea

inΔBDD'
cosB=DB/BD'
√2/2=a/BD'
BD'=a√2
DD'=a-inaltimea

Answer 2

BC=AC/2 (teo unghiuluide 30°)=a/2=l
AB=acos30°=a√3/2 =L
sau AB= √(a²-(a/2)²)=a√3/2=L

m∡(BD', (ABC))=m∡(BD', DD')=45°⇒D'DB dre[ptunghic isoscel in D, D"-DB=AC(diagonale in dreptunghi)=a=h