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The angle of elevation of the top of a tower at a point on the ground is \( \Large 30 ^{\circ} \). If on walking 20m towards the tower the angle of elevation becomes \( \Large 60 ^{\circ} \) then the heights of the tower is:

A) 10 m
B) \( \Large \frac{10}{\sqrt{3}} m \)
C) \( \Large 10\sqrt{3} m \)
D) None of these

Correct Answer:



C) \( \Large 10\sqrt{3} m \)

Description for Correct answer:

Let the height of the tower be h.

\( \Large \triangle PAO, \tan 60 ^{\circ} = \frac{h}{OA} \)

=> \( \Large OA = h \cot 60 ^{\circ} \)

= \( \Large \frac{h}{\sqrt{3}} \)

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

=> \( \Large OB = \frac{h}{\frac{1}{\sqrt{3}}} = \sqrt{3}h \)

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

=> \( \Large 20 + \frac{h}{\sqrt{3}} = \sqrt{3}h \)

=> \( \Large h = \frac{20}{\sqrt{3}-\frac{1}{\sqrt{3}}} = \frac{20\sqrt{3}}{2} = 10\sqrt{3} m \)

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

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Similar Questions

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

2). 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:

A). 20 m

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5). From the top of a light house 60 m high with its base at the sea level the angle of depression of a boat is \( \Large 15 ^{\circ} \). The distance of the boat from the foot of light house is:

A). \( \Large \left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)60 m \)

B). \( \Large \frac{\sqrt{3+1}}{\sqrt{3-1}} m \)

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6). Two poles of equal heights stand on either side of a 100 m wide road. At a point between the poles the angles of elevation of the tops of the poles are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \). The height of each pole is:

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8). A kite is flying at an inclination of \( \Large 60 ^{\circ} \) with the horizontal. If the length of the thread is 120 m, then the height of the kite is:

A). \( \Large 60\sqrt{3} m \)

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