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

 May 7, 2024
 #1
avatar+128796 
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The triangle is equilateral...AD is a bisector and  the altitude of ABC

 

                      A

                  

                     24

 

B                   D                 C

 

Angle  BAD  = 30

BD  =  24/sqrt 3

BC  =  2 * 24 /sqrt 3 =   48/ sqrt 3 =   16sqrt 3

 

[ABC ]  = (1/2) BC * AD  =  (1/2) (16sqrt 3) (24)  =  192 sqrt 3

 

cool cool cool

 May 7, 2024

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