All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Cube Angle (Posted on 2004-08-04) Difficulty: 2 of 5

Can you say what angle is made by the two red lines drawn on two sides of the cube as shown in the illustration?

See The Solution Submitted by SilverKnight    
Rating: 2.4167 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Two solutions | Comment 7 of 14 |

There is the logical and elegant explanation that if you connect the two endpoints of the red lines in the diagram, you will get an equilateral triangle.  If you turn the cube around, you will see each angle is exactly the same, and since the triangle is planar, it is equilateral.  The angles are 60 degrees for an equilateral triangle.

For those who can't imagine the above, I have enough knowledge about vector geometry to solve this.  Making the intersection of the two lines the origin and each red line a vector, I can use the dot product to determine the angle.

The two vectors are (1,-1,0) and (0,-1,-1).  The dot product is 1*0+-1*-1+0*-1=1.  Since the dot product is also cos(angle)*magnitudes, cos(theta)*2=1
Solving, cos(theta)=.5 and theta=60 degrees.

Edited on August 5, 2004, 1:48 pm
  Posted by Tristan on 2004-08-05 13:47:52

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information