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SSC CHSL Model Paper 7

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Question : 49 of 100

Marks: +1, -0

From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°, respectively. What is the height of the tower?

400m
$400\sqrt{3}$ m
$\frac{400}{\sqrt{3}}$ m
None of these

Solution:

In ΔACB, tan 30° =

\frac{200-h}{x} = \frac{1}{\sqrt{3}}

=\frac{500-h}{x}

⇒

x = (200-h)\sqrt{3}

....(i)

In ΔADE,

\tan 45^{\circ} = \frac{200}{x}

⇒

1 = \frac{200}{x} \Rightarrow x = 200\,\mathrm{m}

From Eq. (i)

200 = (200 - h)\sqrt{3}

⇒

h = 200\left(\frac{\sqrt{3} - 1}{\sqrt{3}}\right)\mathrm{m}

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