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When the elevation of sun changes from \( \Large 45 ^{\circ} \) to \( \Large 30 ^{\circ} \) the shadow of a tower increases by 60 m, The height of the tower is:

A) \( \Large 30\sqrt{3} m \)
B) \( \Large 30 \left(\sqrt{2} + 1\right) m \)
C) \( \Large 30 \left(\sqrt{3} - 1\right) m \)
D) \( \Large 30 \left(\sqrt{3} + 1\right) m \)

Correct Answer:




D) \( \Large 30 \left(\sqrt{3} + 1\right) m \)

Description for Correct answer:

Let the height of the tower be h.

\( \Large In \triangle BCD, \tan 45 ^{\circ} = \frac{h}{BC} \)

=> BC = h

\( \Large In \triangle ABD, \tan 30 ^{\circ} = \frac{h}{AB} \)

=> \( \Large AB = \frac{h}{\tan 30 ^{\circ} } \)

=> \( \Large AB= \sqrt{3}h => AC+BC=\sqrt{3}h \)

=> \( \Large 60 + h = \sqrt{3}h \) [using (i)]

=> \( \Large h = \frac{60}{\sqrt{3}-1} = \frac{60 \left(\sqrt{3}+1\right) }{2} = 30 \left(\sqrt{3}+1\right) m \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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Similar Questions

1). A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \( \Large 60 ^{\circ} \) when he retire 40 m from the bank he finds the angle to be \( \Large 30 ^{\circ} \). The breadth of the river is:

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