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…

A balloon is moving up in air vertically above a point A on the ground. When it is at a height $\displaystyle \mathrm{h}_1$, a girl standing at a distance d (point B) from A (see figure) sees it at an angle $\displaystyle 45$° with respect to the vertical. When the balloon climbs up a further height $\displaystyle \mathrm{h}_2$, it is seen at an angle $\displaystyle 60$° with respect to the vertical if the girl moves further by a distance $\displaystyle 2.464$ d (point C ). Then the height $\displaystyle \mathrm{h}_2$ is (given $\displaystyle \tan 30^{\circ}=0.5774$ ) :