Question

A square pyramid has vertices at A (1,0,0), B (0,1,0), C (-1,0,0) and D (0,-1,0) and...

A square pyramid has vertices at A (1,0,0), B (0,1,0), C (-1,0,0) and D (0,-1,0) and E (0,0,-1).

Find the angle between the face ABE and the base.

Find the angle between the faces ABE and ADE.

Math   Algebra   
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Answer #1

The geometry would resemble that like in figure above.

Clearly, ABCD forms the base of the pyramid and E the vertex. Each side of the pyramid is 21/2.

The angle between side ABE and the base is the angle of the equilateral triangle formed by the faces with the base. Since all faces are equilateral, this angle is 60o . So angle between the face ABE and base is 60o.

Also, the angle between two faces is 90o. since each face is aligned with the base. Thus angle between faces ABE and ADE is 90o.

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