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please find the side length of an equilateral triangle

Albert

Well-known member
Jan 25, 2013
1,225
P is an inner point of equilateral triangle ABC ,
given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
P is an inner point of equilateral triangle ABC ,
given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle
Rotate the trianlge by 60 degrees about the point C. Let $P'$ be the new position of $P$. Then $\angle P'PA=90$. Thus we get a triangle $CPA$ with $\angle CPA=150$ and $PC=3, PA=4$. To find $AC$.
 

Albert

Well-known member
Jan 25, 2013
1,225
solution :

side length.jpg