# Find the angle in a Tetrahedron

• Apr 25th 2009, 09:15 AM
beq!x
Find the angle in a Tetrahedron
The point $\displaystyle P$ is the midpoint of the altitude of the regular Tetrahedron. $\displaystyle P$ is linked with $\displaystyle A , B$ of the base of Tetrahedron with segments $\displaystyle PA$ and $\displaystyle PB$.
Find the angles between these segments.
• Apr 25th 2009, 05:04 PM
Nacho
Attachment 11097

We say tha size of each one triangule is $\displaystyle l$, now $\displaystyle AC=CF=CB$ hence $\displaystyle CB = \frac{{l\sqrt 3 }} {3} \Rightarrow DC = \frac{{l\sqrt 6 }} {3} \Rightarrow PC = \frac{{l\sqrt 6 }} {6}$

for other size

$\displaystyle PC^2 + CB^2 = PB^2 \Rightarrow PB = \frac{{\sqrt 2 l}} {2}$

but: $\displaystyle \sin \alpha = \frac{{GB}} {{PB}} = \frac{{\frac{l} {2}}} {{\frac{{\sqrt 2 l}} {2}}} = \frac{{\sqrt 2 }} {2} \Rightarrow \alpha = \frac{\pi } {4} \Leftrightarrow \measuredangle APB = \frac{\pi } {2}$
• Apr 25th 2009, 11:50 PM
beq!x
Quote:

Originally Posted by Nacho

is this a regular tetrahedron ?
i thought that a regular tetrahedron is a regular 3 sides pyramid :confused:
• Apr 26th 2009, 07:35 AM
Nacho
Quote:

Originally Posted by beq!x
is this a regular tetrahedron ?
i thought that a regular tetrahedron is a regular 3 sides pyramid :confused:

Tetrahedron - Wikipedia, the free encyclopedia :)