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

Question

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 $2.464 d$ (point C). Then the height $h_{2}$ is (given $\tan 30 ° = 0.5774$ ):

TestHub · Accepted Answer

t 45 = h 1 d h 1 = d .......(i) h 1 + h 2 d + 2 . 464 d = tan 30 ° = 1 3 = 0 . 5774 h 1 + h 2 = ( 3 . 464 ) d × 0 . 5774 h 1 + h 2 = 2 d .......(ii) ∴ h 2 = d

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