Vectors & 3D Geometry
Dihedral angle between faces of regular tetrahedron
MJAT_TS5_P1
Grade 12
Question:
**Paragraph (continued):** The angle between two adjacent faces of the tetrahedron is $\cos^{-1}\left(\dfrac{K_1}{K}\right)$. Then $K$ is:
Step-by-Step Solution
Key Concept: The dihedral angle $\theta$ between two faces of a regular tetrahedron: $\cos\theta = 1/3$. So $\theta=\cos^{-1}(1/3)$.
$K=\mathbf{3}$ (dihedral angle $=\cos^{-1}(1/3)$).
Correct Answer: 3