Question

An observer finds that the angular elevation of a tower is A. On advancing 3 m towards the tower the elevation is 45∘ and on advancing 2 m nearer, the elevation is (90∘−A). The height of the tower is

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Answer 1

Step-by-step explanation:

Let PQ be the tower of height h

∠PAQ=A,∠PBQ=45

o

and ∠PCQ=90

o

−A

AB=3,BC=2

⇒3=AB=PA−PB=hcotA−h

and 2=BC=PB−CP=h−htanA

∴

h

h+3

=cotA,

h

h−2

=tanA

∴

h

h+3

.

h

h−2

=1⇒h

2

+h−6=h

2

⇒h=6 m