answer keeps coming out wrong and I posted about a similiar

answer keeps coming out wrong and I posted about a similiar question on here and the reply gave a wrong answer as well. The person who answered my previous question also has an answer that was the correct answer but divided by 3 and i can not figure out why no one or i can figure these types of questions out ?

The cross-section of a nuclear power plant\'s cooling tower is in the shape of a hyperbola. Suppose the tower has a base diameter of 162 meters and the diameter at its narrowest point, 48 meters above the ground, is 54 meters. If the diameter at the top of the tower is 108 meters, how tall is the tower? The tower is about meters tall. The tower is about meters tall. (Round to one decimal place as needed.)

Solution

Solution: 2a = 54, 2b = ?

a = 54/2=27, 162/2=81, 108/2 = 54

At the base point (81, 0)

           x²/27² - (y-48)²/b² = 1
or       81²/27² - (0-48)²/b²=1
- (48)²/b² = 1 - 81² /27²

Thus        b² = 288.

Now, putting the values of a and b at the top (x,y ) = (54, y-48).
Thus   54² /27² - (y-48)² /288 = 1

            (y-48)² /288 = 54² /27² -1

             (y-48)² /288 = 3

              (y-48)² = 3*288

               (y-48)² = 864

(y-48) = 29.4

y = 29.4+48

   or    y = 77.4 meter.

Hence the height of the tower is 77.4 meter.                      Ans