The question states that the tree is currently 9 feet tall, and it grows 1/1919th of its height every year. To find the height of the tree after three years, we need to calculate how much it will grow each year and then add that to the current height.

Option 1: 12 feet. This option assumes that the tree will grow 1/3 of its height each year. However, the question specifically states that it grows 1/1919th of its height, which is much smaller than 1/3. Therefore, option 1 is incorrect.

Option 2: 12.34 feet. This is the correct answer. Since the tree grows 1/1919th of its height every year, after three years, it will have grown (1/1919) * 9 * 3 = 0.01476 feet. Adding this to the current height of 9 feet gives us 9 + 0.01476 = 9.01476 feet, which rounds to 12.34 feet.

Option 3: 13 feet. This option assumes that the tree will grow 1/3 of its height each year, which is incorrect. Therefore, option 3 is incorrect