Question

Two hoardings of cleanness are put on a 80m wide road on two poles which are opposite
sides of road and are of some height. The angle of elevation of both pole; from a pointat
theroad is 60' and 30'. Find the height of poles and distance of poles from that point
​

Answer 1

Step-by-step explanation:

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