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ABCDEFGH, refer to image in the link, is a cube. Find the sine of ∠GAC.

 

https://latex.artofproblemsolving.com/4/e/9/4e96fce20bc93f1aeeb0dea0d9cad167be87c62d.png

 Nov 9, 2019
 #1
avatar+104932 
+2

 GAC  will form a right triangle

 

Let  GC  =  the  side of the cube  = S

Then AC  will = S√2

And  GA  = S√3

 

So.....GA  is the hypotenuse   and   AC  and  GC will form the legs

 

So

 

sin GAC   =   GC / GA   =    S   / [ S√3 ]  =  1  /√ 3 

 

[ To find the angular measure  use  arcsin (1/ √3)  ≈  35.26° ]

 

 

cool cool cool

 Nov 9, 2019

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