50
From the top of a building $60$ m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be $30^\circ$ and $60^\circ$ respectively.
(i) Find the horizontal distance between the building and the lamp post.
(ii) Find the distance between the tops of the building and the lamp post.
(i) Find the horizontal distance between the building and the lamp post.
(ii) Find the distance between the tops of the building and the lamp post.
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Correct figure Let AB be the building and CD be the lamp post of height '$h$' m. (i) $\tan 60^\circ = \frac{60}{x} = \sqrt{3} \Rightarrow x = 20\sqrt{3}$ m or AC = $20\sqrt{3}$ m (ii) $\cos 30^\circ = \frac{x}{BD} = \frac{\sqrt{3}}{2} \Rightarrow BD = \frac{2\times 20\sqrt{3}}{\sqrt{3}} = 40$ m