Three (3) times the screen height is a more realistic number. It used to be 3 to 5 times when taking into account standard definition but HD format allows for a closer seating position. At 14 feet from the screen I'd look at a front projection unit.
Here's a few dimensions of 1.78:1 (16:9) projection screens and the 3 times seating distances.
82" diag = 40.5" high x 72" wide (40.5 x 3 = 121.5" or 10' 1.5")
92" diag = 45" high x 80" wide (45 x 3 = 135" or 11' 3")
100" diag = 49" high x 87" wide (49 x 3 = 147" or 12" 3")
110" diag = 54" high x 96" wide (54 x 3 = 162" or 13' 6")
123" diag = 60" high x 107" wide (60 x 3 = 180" or 15')