A balloon is moving up in air vertically above a point $$A$$ on the ground. When it is at a height $$h_1$$, a girl standing at a distance $$d$$ (point B) from $$A$$ (see figure) sees it at an angle $$45^\circ$$ with respect to the vertical. When the balloon climbs up a further height $$h_2$$, it is seen at an angle $$60^\circ$$ with respect to the vertical if the girl moves further by a distance $$2.464\,d$$ (point C). Then the height $$h_2$$ is (given $$\tan 30^\circ = 0.5774$$):