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36. Two poles of equal heights are standing opposite each other on either side of the road,
which is 80m wide. From a point between them on the road angle of elevation of the
top of the poles are 60°and 30° respectively. Find the height of the poles and the
distance of point from the poles.
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Class-IX Maths
Asked by Rakshana Maria
Dec 5, 2014
Find the height of the poles and the distances of the point from the poles.
Two poles of equal heights are standing opposite each other on either side of the roads, 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.
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Ramesh
Member since Apr 1, 2014
Let AB and CD be the two poles of equal height and their heights be H m. BC be the 80 m wide road. P be any point on the road. Let CP be x m, therefore BP = (80 – x) . Also, ∠APB = 60° and ∠DPC = 30° In right angled triangle DCP, Tan 30° = CD/CP ⇒ h/x = 1/√3 ⇒ h = x/√3 ---------- (1) In right angled triangle ABP, Tan 60° = AB/AP ⇒ h/(80 – x) = √3 ⇒ h = √3(80 – x) ⇒ x/√3 = √3(80 – x) ⇒ x = 3(80 – x) ⇒ x = 240 – 3x ⇒ x + 3x = 240 ⇒ 4x = 240 ⇒ x = 60 Height of the pole, h = x/√3 = 60/√3 = 20√3. Thus, position of the point P is 60 m from C and height of each pole is 20√3 m.
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Answer:
Same as above friend
Step-by-step explanation:
1 st do as directed in the above explanation