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Help plz with geometry

 

In triangle ABC, the angle bisector of angle BAC meets BC at D.  If angle BAC = 60, angle ABC = 60, and AD = 24, then find the area of triangle ABC.

 Feb 22, 2023
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So this should be an equilateral triangle since two angles are 60 degrees.  This means BD + CD = BC = AB =DC.  The sin(60) is sqrt(3)/2.  So if AD=24, then each side of the equilateral triangle is 16sqrt(3).  Doing the triangle area formula of (BH)/2, we get 192 sqrt(3).  

 Feb 22, 2023

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