two cars are opposite side of a tower 9 km and 4 km away from the tower if it makes angle of elevation complementary to each other on some straight line find the height of the tower
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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
AA……..(1)
From ΔABQ
tan(90−θ)=
BQ
AA(∵tan(90−θ)=cotθ)
(cotθ=
tanθ
1 )
We get,
cotθ= AB BB = AB ……..(2)
by equation (1) & (2) we get,
a....AB
= AB.....b
⇒AB ...2
=ab⇔AB= ab
∴AB=height= ab
Hence proved.
Step-by-step explanation:
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