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Geometry homework

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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

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pls be more descriptive when the say the centroid is...?

Jan 14, 2019
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fixed it

Mathguru  Jan 14, 2019
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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
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Good job, TwentyFour.....Welcome aboard  !!!!   CPhill  Jan 15, 2019