Q2 of 58 Page 665

If the height of a vertical pole is √3 times the length of its shadow on the ground then the angle of elevation of the sun at that time is

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Let AB be the pole and BC be the shadow. Join A and C. We get a right-angled triangle right angled at B. The angle of elevation of the sun is ∠ ACB (= θ, say). We use the trigonometric ratio tan for the triangle taking AB as height and BC as the base. By the problem, AB = √3BC.


In ∆ABC,



or,


θ = 60°


since we know that tanθ is √3 whenever θ = 60°.


So, the correct option is (C).

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33

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60° respectively. Find

(i) the horizontal distance between AB and CD,


(ii) the height of the lamp post,


(iii) the difference between the heights of the building and the lamp post.

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