If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC is

Engineering

Mathematics

problems on height and distance

Question

$\sqrt{3} : 1$

$1 : \sqrt{3}$

$\sqrt{3} : \sqrt{2}$

2 : 3

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h = $\sqrt{3}$ CD

h = BC + CD

$h = \frac{(AB + BC + CD)}{\sqrt{3}}$

$BC = (\frac{\sqrt{3} - 1}{\sqrt{3}}) h$

$AB = (\sqrt{3} - 1) h$

⇒ AB : BC = $\sqrt{3} : 1$