A regular triangular pyramid has all of edges of length 36. What is the angle between any two faces of this pyramid?
I have no idea what to do for this problem. Can someone explain to me what an angle between two faces is?
[Math] Angle Between Two Faces of a Triangular Pyramid
geometry
Related Solutions
I visualized the solution Nick provided:
(I found it because it had used this arrangement to build boats models with a magnet game)
The angle between two planes $\alpha$ and $\beta$, having a line of intersection $r$, is defined as the angle formed by two lines $a\subset \alpha$ and $b\subset\beta$, both perpendicular to $r$ at the same point $M$.
In your case, to find the angle between $OAB$ and $OBC$ you can for instance draw the altitudes $AM$ and $CM$ of those two faces: then the angle is $\angle AMC$. To compute it you can find the lengths of $AM$, $CM$ and $AC$ (by some standard trigonometry) and then use the cosine law to get the angle.
The angle between $OAB$ and $ABCD$ is even easier: if $OK$ is another altitude of face $OAB$, then the angle is just $\angle OKH$, where $H$ is the center of square base.
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Best Answer
The lengths of the sides of the regular tetrahedron are irrelevant.
Hint: Find the vectors from the tetrahedron's center to the center of two faces. Then calculate the angle between them.