Ex 9.1 , 10
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.
Let two poles be AB & CD
So, Length of pole = AB = CD
Also, Length of the road = 80m
So, BC = 80m
Lets point P be a point on the road between poles,
We need to find height of poles i.e. AB & CD
and distance of the point from poles, i.e. BP & CP
Since poles are perpendicular to ground
∠ ABP = 90° & ∠ DCP = 90°
From (1) & (2)
𝐶𝑃/√3 = √3 BP
CP = √3×√3 BP
CP = 3BP
Now,
BC = BP + CP
80 = BP + CP
80 = BP + 3BP
80 = 4BP
4BP = 80
BP = 80/4
BP = 20 m
Now,
CP = BC – BP
CP = 80 – 20
CP = 60 m
From (2)
CD = √3BP
CD = √3 × 20
CD = 20√3 m
Hence,Length of the pole = CD = 20√3 m.
And
Distance of point P from pole CD = CP = 60 m
Distance of point P from pole AB = BP = 20 m

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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