The side opposite the 30o angle is 1/2 W. That is just a property of a 30 - 60 - 90 triangle. Use that fact to set up the pythagorean relationship.
w^2 = (1/2 w)^2 + (7 * sqrt(3)) ^2
w^2 = 1/4 w^2 + 49*3
w^2 = 1/4 w^2 + 147
3/4 w^2 = 147
w^2 = 147 * 4/3
w^2 = 49 * 4 = 196
w = sqrt (196)
w = 14
