Angles in a Cube I from Interactive Mathematics Miscellany and Puzzles

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Angles in a Cube I

Let denote the vertices of a cube ABCD (for the bottom face) and A'B'C'D' (for the top face), with A' above A, etc. What is the angle AB'C?

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Solution

Add to the picture the side AC. As all three segments AB', B'C and AC are the diagonals of equal squares, they are equal and, thus, form an equalteral triangle, implying that angle AB'C is 60°.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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