Respuesta :
Let AB = Side of the tetrahedron = s
Then BM = AM = s * sqrt(3)/2
Using the Law of Cosines,
we have thatAB^2 = BM^2 + AM^2 - 2 (BM)(AM) cos AMBs^2 = (3/4)s^2 + (3/4)s^2 - 2 ( 3/4)s^2 cos AMBs^2 = (3/2)s^2 - (3/2)s^2 cos AMB[ 1/2]s^2 / [ (3/2) s^2 ] = cos AMB[ 1/2] / [3/2] = cos AMB1/3 = cos AMB
In geometry, a tetrahedron, also referred to as a triangular pyramid, is a polyhedron composed of 4 triangular faces, six straight edges, and four vertex corners. The tetrahedron is the best of all the everyday convex polyhedron and the best one that has fewer than five faces. The tetrahedron is the best polyhedron that has 4 faces. it's also the best easy polyhedron that has no polyhedron diagonals (i.e. no face diagonals or space diagonals). An isosceles tetrahedron is a special case of the general tetrahedron for which all four of the triangular faces are congruent. A tetrahedron is a platonic stable which has 4 triangular faces, 6 edges, and 4 corners. it's also referred to as a 'Triangular Pyramid' due to the fact the bottom of a tetrahedron is a triangle. A tetrahedron is different from a rectangular pyramid, which has a square base. The tetrahedron is one sort of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the bottom to a common factor. inside the case of a tetrahedron the base is a triangle (any of the 4 faces can be taken into consideration the bottom), so a tetrahedron is likewise referred to as a "triangular pyramid".
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