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?

beastrohit
Nov 28, 2018

#1**+1 **

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

CPhill
Nov 28, 2018