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In triangle ABC, the acute angles are angle B =60 degrees and angle C =30 degrees. The centroid of triangle ABC is G. If AB=1, what is AG?

 Nov 28, 2018
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Since AB = 1

Then the side opposite angle A  = BC =  2   = the hypotenuse

And the side opposite angle B = AC  = sqrt(3)

 

 So....Let A = (0,0)    B = (1,0)    C = (0, sqrt(3) )

 

Call the midpoint of BC, T

And the coordinates of this point are   ( 1/2 , sqrt(3)/2)

So....AT is a median of triangle ABC

And centroid G will be (2/3) of the distance from A to T

And this distance is  (2/3)sqrt [ (1/2)^2 + (sqrt(3)/2)^2 ] = (2/3) sqrt [ 1/4 + 3/4] =

 

(2/3) sqrt (1) =     (2/3)  = AG

 

 

cool cool cool

 Nov 28, 2018

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