+159 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?
+128472
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
