bonanova Posted October 14, 2008 Report Share Posted October 14, 2008 (edited) This problem can be done without resorting to pencil and paper. Mentally mark one of the corners of a cube as A. Mentally draw a line from A diagonally across a face of the cube to corner B. [Edit] Mentally draw a line from A diagonally across a different face of the cube to corner C. [Edit] How many degrees are there in the angle BAC? Edited October 14, 2008 by bonanova Clarification about where the lines are drawn from Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2008 Report Share Posted October 14, 2008 This problem can be done without resorting to pencil and paper. Mentally mark one of the corners of a cube as A. Mentally draw a line from A diagonally across a face of the cube to corner B. [Edit] Mentally draw a line from A diagonally across a different face of the cube to corner C. [Edit] How many degrees are there in the angle BAC? How about 90º??? Just a question... Corners A & B are on the same face, right??? If this is true, Corner C should be on the opposite face of where A & B are located? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 14, 2008 Author Report Share Posted October 14, 2008 How about 90º??? Just a question... Corners A & B are on the same face, right??? If this is true, Corner C should be on the opposite face of where A & B are located? Corners A and B are on the same face - perhaps the top face. Corners A and C would then share a side face. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2008 Report Share Posted October 14, 2008 Hmmm... 60 degrees? Quote Link to comment Share on other sites More sharing options...
0 Prime Posted October 14, 2008 Report Share Posted October 14, 2008 (edited) A and C are on the same face diagonally. So you have an equilatteral triangle -- the angles are 60 degrees each. Edited October 14, 2008 by Prime Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2008 Report Share Posted October 14, 2008 (edited) To help visualize what's happening... The blue lines connect the diagonals. From A to B, from A to C, and from B to C are all the same length (the diagonal of the cube), so they form an equilateral triangle. Like Prime said, this gives you 60 degrees. Edited October 14, 2008 by Dragonjest22 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2008 Report Share Posted October 14, 2008 Without looking at the spoilers and doing it entirely in my head... is 60 degrees, because for the triangle formed, each side is the same length. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 14, 2008 Report Share Posted October 14, 2008 To help visualize what's happening... The blue lines connect the diagonals. From A to B, from A to C, and from B to C are all the same length (the diagonal of the cube), so they form an equilateral triangle. Like Prime said, this gives you 60 degrees. Nice picture! I see you and prime beat me to the answer, well done! Quote Link to comment Share on other sites More sharing options...
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bonanova
This problem can be done without resorting to pencil and paper.
Mentally mark one of the corners of a cube as A.
Mentally draw a line from A diagonally across a face of the cube to corner B. [Edit]
Mentally draw a line from A diagonally across a different face of the cube to corner C. [Edit]
How many degrees are there in the angle BAC?
Edited by bonanovaClarification about where the lines are drawn from
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