A balloon is rising vertically above a fixed point \(A\) on the ground. A girl at point \(B,\) located \(d\) metres from \(A,\) observes the balloon at a height \(h_1\)​ and sees it at an angle of \(45^\circ\) with respect to the vertical. After the balloon ascends an additional height \(h_2,\) the girl walks \(2.464d\) metres further away from point \(A\) to reach point \(C.\) From this new position, she observes the balloon at an angle of \(60^\circ\) with the vertical.  If \(\tan 30^{\circ}=0.5774,\) then what is the value of \(h_2\)​ in terms of \(d \text{?}\)