A balloon is moving up in air vertically above a point $A$ on the ground. When it is a height $h_1,$ a girl standing at a distance d (point B) from A (see figure) sees it at an angle $45°$ with respect to the vertical. When the balloon climbs up a further height $h_2$, it is seen at an angle $60°$ with respect to the vertical if the girl moves further by a distance $2.464 \mathrm{d}$ (point C). Then the height ${\mathrm{h}}_2$ is (given $\tan 30°=0.5774$):