Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60° respectively. The ratio of AB and BC is
Suppose the tower is \( DE \) of height \( h \), where point \( \mathbf{D} \) is on the ground. Then, \[ AD = \frac{h}{\tan 30^\circ} = h \sqrt{3}, \] \[ BD = \frac{h}{\tan 45^\circ} = h, \] \[ CD = \frac{h}{\tan 60^\circ} = \frac{h}{\sqrt{3}}. \] The ratio \[ \frac{AB}{BC} = \frac{h \sqrt{3} - h}{h - \frac{h}{\sqrt{3}}} = \frac{\sqrt{3}}{1}. \]
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