QJEEM08Ma1b9d: JEE Main 2008 Mathematics - Class 12 JEEM08Ma1b9d Solution: is a vertical pole with at the ground level and at the top. man …

Question

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AB

is a vertical pole with

B

at the ground level and

A

at the top.

A

man finds that the angle of elevation of the point

A

from a certain point

C

on the ground is

{60^ \circ }

. He moves away from the pole along the line

BC

to a point

D

such that

CD=7

m. From

D

the angle of elevation of the point

A

is

{45^ \circ }

. Then the height of the pole is :

Accepted Answer

In

\Delta ABC

{h \over x} = \tan {60^ \circ } = \sqrt 3

\Rightarrow x = {h \over {\sqrt 3 }}

In

\Delta ABD{h \over {x + 7}}

= \tan {45^ \circ } = 1

\Rightarrow h = x + 7 \Rightarrow h - {h \over {\sqrt 3 }} = 7

\Rightarrow h = {{7\sqrt 3 } \over {\sqrt 3 - 1}} \times {{\sqrt 3 + 1} \over {\sqrt 3 + 1}}

\Rightarrow h = {{7\sqrt 3 } \over 2}\left( {\sqrt 3 + 1\,m} \right)

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