Question

Two poles of equal heights are standing opposite each other on either

side of the road which is 80m wide. From a point O between them on the

road, the angles of elevation of the top of the poles are 600

and 300

respectively. Find the height of the poles and the distances of the point

from the poles.​

Answer 1

Answer:

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