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Question

On the level ground the angle of elevation of the top of a tower is $$\displaystyle  30^{\circ} $$ On moving 20 m nearer the angle of elevation is $$\displaystyle  60^{\circ} $$. The height of the tower is


A
10m
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B
15m
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C
103 m
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D
20m
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Solution

The correct option is B $$\displaystyle 10\sqrt{3} $$ m
Distance between length of shadows = $$20$$ m when the angle of elevation changes from $$30^{\circ}$$ to $$60^{\circ}$$
Let the length of pole = $$p$$
Length of shadow when angle of elevation = $$30^{\circ}$$
Shadow =$$ p \tan 30 = \dfrac{p}{\sqrt{3}}$$
Length of shadow when angle of elevation = $$60^{\circ}$$
Shadow =$$ p \tan 60 = p\sqrt{3}$$
Distance between the two shadows = $$p \sqrt{3} - \dfrac{p}{\sqrt{3}}$$ = $$20$$
$$3p - p = 20\sqrt{3}$$
$$p = 10\sqrt{3}$$ m

Mathematics

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