Question

D] Two poles of equal heights are standing opposite each other and 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 poles and the
distance of the point from the poles.
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Answer 1

Solution :-

Given : Two poles of equal heights are standing opposite each other and either side of the road, which is 80 m wide.

Let us suppose that ED and AB are the two poles and DB be the width of road C is the point between the two poles. And the length of CD be x m and BC be (80 - x) m

tan 60° = AB/BC

=> √3 = AB/(80 - x)

=> AB = √3(80 - x) ____(i)

tan 30° = ED/CD

=> 1/√3 = ED/x

=> ED = x/√3 _____(ii)

We know that the height of the two poles is equal. i.e., AB = ED

Now, Comparing AB and ED,

=> √3(80 - x) = x/√3

=> 80 - x = x/3

=> 80 = x/3 + x

=> 80 = (x + 3x)/3

=> 240 = 4x

=> x = 60

So, the length of :

CD = x = 60 m

BC = 80 - x = 80 - 60 = 20 m

Height of poles :

AB = ED = x/√3

= 60/√3

= (60 × √3)/(√3 × √3)

= 60√3/3 = 20√3 m