,The angle of elevation of the top of chimney from two points p and q on the ground are 30° and 45°. Respectively the ratio of the distance of p and q from the top of the chimney is (2)
√2:1
1:√2
2√2:1
2:1
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1
Answer:
Given,
the angle of elevation of the top of the tower from two points P & Q is at a distance of a & b.
Also given, to prove that the tower
height=
ab
(∵ complementary angle =(90
o
−θ))
From ΔABP
tanθ=
BP
AB
=
a
AB
……..(1)
From ΔABQ
tan(90−θ)=
BQ
AB
(∵tan(90−θ)=cotθ)
(cotθ=
tanθ
1
)
We get,
cotθ=
AB
BQ
=
AB
b
……..(2)
by equation (1) & (2) we get,
a
AB
=
AB
b
⇒AB
2
=ab⇔AB=
ab
∴AB=height=
ab
Hence proved.
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The angle of elevation of the top of chimney from two points p and q on the ground are 30° and 45°. Respectively the ratio of the distance of p and q from the top of the chimney is (2) √2:1. 1:√2.
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