Krish every thing is right with your answer except that dA/at is -1/48 radian per sec instead of degrees per second.

And there is another way to look at this problem

dA/dt==(v tangential)/r  (r is the radius of kite from man holding it ie. 120 m)

V tangential is equall to 5sin(30)=2.5m/s

Therefore dA/at=1/48 (in magnitude)