Question

The angle of elevation of the top of the tower from two points distance a and b from its foot are complementary. prove that the height of the tower is root ab.
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Answer 1

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.

thanks

Answer 2

Answer:

above answer is definitely correct