document.write( "Question 907051: A diagonal of a cube is a line segment of maximum length whose endpoints are vertices of the cube. To the nearest degree, what is the angle of intersection Ѳ, 0 < Ѳ <= 90° between two distinct diagonals of the same cube?\r
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Algebra.Com's Answer #550172 by Edwin McCravy(20056)\"\" \"About 
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document.write( "This cube is drawn in perspective so don't expect all \r\n" );
document.write( "the right angles to look like right angles.\r\n" );
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document.write( "Suppose each edge of the cube is 1 unit long. Then since \r\n" );
document.write( "triangle ABC is a right triangle, its hypotenuse AC, the \r\n" );
document.write( "red line, is \"sqrt%282%29\" by the Pythagorean theorem.\r\n" );
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document.write( "The triangle ACD is also a right triangle, and by the\r\n" );
document.write( "Pythagorean theorem on it we get that AD˛=AC˛+CD˛ which\r\n" );
document.write( "leads to AD = \"sqrt%283%29\".\r\n" );
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document.write( "Now we draw in the green diagonal CE, and also the red line DE.\r\n" );
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document.write( "Now let's remove rectangle ACDE.\r\n" );
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document.write( "We want to find angle AOE.\r\n" );
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document.write( "tan(∠DAC) = \"EA%2F%28AC%29=1%2Fsqrt%282%29\"\r\n" );
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document.write( "∠DAC = 35.26438968°\r\n" );
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document.write( "∠EAD = 90°-35.26438968° = 54.73561032°\r\n" );
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document.write( "Since triangle AOE is isosceles, so ∠AEO = ∠EAD = 54.73561032°.\r\n" );
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document.write( "So Since the sum of the three angles of triangle AOE, \r\n" );
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document.write( "∠AOE = 180° - ∠AEO - ∠EAD = 180° - 2(54.73561032°) = 70.52877937°\r\n" );
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document.write( "That's the answer, and we can draw in the other two diagonals of the cube.\r\n" );
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document.write( "All three diagonals intersect at the same point. And the acute angle \r\n" );
document.write( "between any two of the three adjacent diagonals is 70.52877937°.  \r\n" );
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document.write( "Edwin
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