cube problem

**daydreembelievr** · November 7th 2008, 07:26 PM

Suppose each edge is 6 inches long. Find the measure of the angle formed by diagonal GB and edge GC.
I can do similar problems but the angle on this one is killing me. Can someone please help m figure it out? thanks sooooo much

**Soroban** · November 7th 2008, 07:52 PM

Hello, daydreembelievr!

Suppose each edge is 6 inches long.
Find the measure of the angle formed by diagonal $GB$ and edge $GC$ .

Triangle $BCG$ is a right triangle.

Code:

            * B
           /|
          / |
         /  |   _
        /   | 6√2
       /    |
      /     |
     / θ    |
  G *-------* C 
        6

$GC$ is an edge of the cube: . $GC \:=\:6$

$BC$ is the diagonal of a face: . $BC \:=\:6\sqrt{2}$

Then: . $\tan\theta\:=\:\frac{6\sqrt{2}}{6} \:=\:<br /> \sqrt{2}\quad\Rightarrow\quad \theta \:\approx\:54.7^o$

**daydreembelievr** · November 7th 2008, 07:54 PM

I was having so much trouble visualizing it in 2D, but now that makes a lot of sense. thanks so much

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