QJEEM15Ma6b74: JEE Main 2015 Mathematics - Class 12 JEEM15Ma6b74 Solution: If the angles of elevation of the top of a tower from three…

Question

Verified Solution • 2025–26 Session moderate

If the angles of elevation of the top of a tower from three collinear points

A, B

and

C,

on a line leading to the foot of the tower, are

{30^ \circ }

,

{45^ \circ }

and

{60^ \circ }

respectively, then the ratio,

AB:BC,

is :

Accepted Answer

As

PB

bisects

\angle APC,

therefore

AB

:

BC

=PA:PC

Also in

\Delta APQ,\sin {30^ \circ } = {h \over {PA}} \Rightarrow PA = 2h

and in

\Delta CPQ,

\sin {60^ \circ } = {h \over {PC}} \Rightarrow PC = {{2h} \over {\sqrt 3 }}

\therefore

AB:BC = 2h:{{2h} \over {\sqrt 3 }} = \sqrt 3 :1

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