Karen measured her high as 59 inches that is 27 inches more than half her older sister’s height. How tall is her older sister?

Let x be Karen's older sister's height.

Karen = (x/2) + 27
59 = (x/2) + 27
59 - 27 = (x/2)
32 = (x/2)
x = 2 * 32
x = <<64=64>>64 inches
Karen's older sister is 64 inches tall. Answer: \boxed{64}.