Karen measured her height as 59 inches. That is 27 inches more than half her older sister's height. How tall is her older sister? (1 poinf) inches.

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

Karen's height is x/2 + 27 inches.
So, x/2 + 27 = 59.
Thus, x/2 = 59 - 27 = 32.
Therefore, the height of Karen's older sister is x = 64 inches. Answer: \boxed{64}.