Math, asked by rockinggirl4322, 10 days ago

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

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Answers

Answered by claxmi190gmailcom
1

Answer:

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>>Some Applications of Trigonometry

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>>Two poles of equal heights are standing

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Two poles of equal heights are standing opposite to each other, on either side of the road, which is 80m wide. From a point between them on the road, the angles of elevation of top of the poles are 60

o

and 30

o

respectively. Find the height of the poles.

Medium

Solution

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Given that:

∠APB=60

,∠CPD=30

,AC=80m

To find:

The height of the pole=AB=CD=?

Solution:

Let AB and CD be the two poles of equal height and P be the point on the road between the poles.

In △APB,

tan60

=

AP

AB

or, AP=AB×

tan60

1

or, AP=

3

AB

−−−−−−−(i)

In △PCD,

tan30

=

CP

CD

or, CP=CD×

tan30

1

or, CP=

3

CD=

3

AB ∵AB=CD −−−−−−−(ii)

Adding eqn. (i) and eqn. (ii) we get,

AP+CP=

3

AB

+AB

3

or, AC=AB(

3

+

3

1

)

or, 80m=4

3

AB

or, AB=20

3

m

Therefore, height of the pole=20

3

m=34.64m

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