Question

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.​

Answer 1

Answer:-

→ Let AB and CD be the poles of equal height.

→ O is the point between them from where the height of elevation taken.

→ BD is the distance between the poles.

According to the diagram, AB = CD,

OB + OD = 80 m

Now,

In right ΔCDO,

tan 30° = CD/OD

1/√3 = CD/OD

CD = OD/√3 → (1)

In right ΔABO

tan 60° = AB/O

√3 = AB/(80 - OD)

AB = √3(80 - OD)

AB = CD [Given]

√3(80-OD) = OD/√3 [Using eq (1)]

3(80-OD) = OD

240 – 3 OD = OD

4 OD = 240

OD = 60

Substituting the value of OD in eq (1)

CD = OD/√3

CD = 60/√3

CD = 20√3 m

Also, wkt:-

OB + OD = 80 m

⇒ OB = (80-60) m = 20 m

Therefore, 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

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