A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a p...

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flag-staff are respectively \( 60^{\circ} \) and \( 45^{\circ} \). Find the height of the flag-staff and that of the tower.
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