JEE Main · 2008 · 27 Apr 2008 · Offline · Heights and Distances

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

6 0^{\circ}

. He moves away from the pole along the line

B C

to a point

D

such that

C D = 7 m

. From

D

the angle of elevation of the point

A

4 5^{\circ}

. Then the height of the pole is

Answer: (B)

Solution

Let the pole have height

h

and let

C

be at distance

x

from its foot. From

C

the elevation is

6 0^{\circ}

, so

h = x tan 6 0^{\circ} = x 3

, and from

D

, a further

7 m

away, the elevation is

4 5^{\circ}

, so

h = x + 7

. Equating,

x 3 = x + 7

gives

x = \frac{7}{3 - 1} = \frac{7 ( 3 + 1 )}{2}

, and therefore

h = x 3 = \frac{7 3}{2} (3 + 1) m

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option