Math, asked by vaibhavrajput049, 5 months ago

The angle of the elevation of the top of a tower from two points on the ground at a distance is 'a' metre and 'b' metres from the base of the tower and in the same straight line with it are complementary. Then the square of the height of the tower is :-​

Answers

Answered by parthmongia200559
0

Answer:

Step-by-step explanation:

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.

Answered by sehejarora75
0

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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