Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is?

Question

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is A) 30&deg; B) 60&deg; C) 45&deg; D) 90&deg;

Accepted Answer

The object formed by four equilateral triangles is a regular tetrahedron. The angle between any two faces of a regular tetrahedron is known as the dihedral angle. This angle can be calculated using various methods, typically involving vector geometry or trigonometry. The cosine of the dihedral angle (θ) of a regular tetrahedron is 1/3. Therefore, θ = arccos(1/3). Arccos(1/3) is approximately 70.53 degrees. Reviewing the options, 60&deg; is the closest common incorrect answer if one assumes the face angles, but the dihedral angle is different.

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