special right triangles

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The altitude, 1/2 base length  and the  side form  a 30-60-90  right triangle

The  altitude  is  opposite  a 60° angle

The side is  opposite a  90° angle

Using the relationships in this triangle :

The  side =   2 /sqrt (3)  * 27  =    54/sqrt (3)   =  54sqrt (3) / 3  =  18sqrt (3)