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In a regular tetrahedron, prove that ang...

In a regular tetrahedron, prove that angle `theta` between any edge and the face not containing that edge is given by `cos theta = 1/sqrt3`.

A

`1//6`

B

`1//9`

C

`1//3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let OABC be the tetrahedron. Let G be the centorid of the face OAB, then `GA=1/sqrt(3)AC`.

Then `costheta=(GA)/(CA)=1/sqrt(3)`
`therefore cos^(2)theta=1/3`
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