# Find the angle in a Tetrahedron

• April 25th 2009, 10:15 AM
beq!x
Find the angle in a Tetrahedron
The point $P$ is the midpoint of the altitude of the regular Tetrahedron. $P$ is linked with $A , B$ of the base of Tetrahedron with segments $PA$ and $PB$.
Find the angles between these segments.
• April 25th 2009, 06:04 PM
Nacho
Attachment 11097

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

for other size

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

but: $
\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}
$
• April 26th 2009, 12:50 AM
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:
• April 26th 2009, 08:35 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 :)