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In triangle ABC the acute angles are b=60 and c=30. The centoride of abc is G. If ab=1 what is ag

 

Help asap.

 Jan 14, 2019
edited by Mathguru  Jan 14, 2019
 #1
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pls be more descriptive when the say the centroid is...?

 Jan 14, 2019
 #2
avatar+7 
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fixed it

Mathguru  Jan 14, 2019
 #3
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Since \(\triangle ABC\) is a 30-60-90 triangle and \(\overline{AB}\) is 1, \(\overline{AC}\) is \(\sqrt{3}\) and \(\overline{BC}\) is 2. Let the intersection of the ray \(\overline{AG}\) through \(\overline{BC}\) be D. Becuase \(\overline{AD}\) is a median, it divides \(\overline{BC}\) into 2 equal parts. Therefore, \(\overline{BD}\) is 1. Now, we can say that \(\triangle BAD\) is equilateral because it is isoceles, and one of the angles is 60. As such, \(\overline{AD}\) is 1. 

 

The centroid divides medians into 2 parts ratio 1:2, so \(\overline{AG}\) is \(\boxed{\frac{2}{3}}\).

 

First post, How'd I do?

 

-24

 Jan 15, 2019
 #4
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Good job, TwentyFour.....Welcome aboard  !!!!

 

 

 

cool cool cool

CPhill  Jan 15, 2019

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