Question

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From point between them on the road, the angles of elevation of the top of poles are 60° and 30°, respectively. Find the height of the poles and the distance of the point from the poles.


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Answer 1

Given:-

$\rightsquigarrow$ Let AB and CD be the poles of equal height.

$\rightsquigarrow$ O is the point between them from where the height of elevation taken. BD is the distance between the poles.

ŤÓ find:-

Find the height of the poles and the distance of the point from the poles.

Solution:-

As per above figure, AB = CD,

$\rightsquigarrow$ OB + OD = 80 m

Now,

In right ΔCDO,

 tan 30° = CD/OD

⇝$\rightsquigarrow$  1/√3 = CD/OD

⇝$\rightsquigarrow$  CD = OD/√3......(Equation1)

Again,

In right ΔABO,

⇝ $\rightsquigarrow$ tan 60° = AB/OB

⇝ $\rightsquigarrow$ √3 = AB/(80-OD)

⇝$\rightsquigarrow$  AB = √3(80-OD)

⇝ $\rightsquigarrow$ AB = CD (Given)

⇝ $\rightsquigarrow$ √3(80-OD) = OD/√3 (Using equation1)

⇝ $\rightsquigarrow$ 3(80-OD) = OD

⇝ $\rightsquigarrow$ 240 – 3 OD = OD

⇝$\rightsquigarrow$  4 OD = 240

⇝ $\rightsquigarrow$ OD=60

Putting the value of OD in equation (1)

⇝ $\rightsquigarrow$ CD = OD/√3

⇝$\rightsquigarrow$  CD = 60/√3

⇝ $\rightsquigarrow$ CD = $\red{\dfrac{20}{\sqrt{3}}}$ m

Also,

⇝ $\rightsquigarrow$ OB + OD = 80 m

$\rightsquigarrow$ OB = (80-60) m = 20 m

ÄÑŠWÊŘ::-

Thus, the height of the poles are 20√3 m and distance from the point of elevation are 20 m and 60 m respectively.

Answer 2

Step-by-step explanation:

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