Math, asked by anupriyabishnoi, 9 months ago

two poles of equal height are standing opposite to each other on either side of a road which is 100m wide from a point between them on the ground. The angle of elevation of tops of poles are 30 degrees and 60 degrees. The height of each pole in mt wiil be?

Answers

Answered by mirajha13
0

Answer:

Step-by-step explanation:

According to the given information draw a figure

[ Refer the attachment ]

Let the to poles be be AB and DE

Height of AB = Height of CD

Distance between AB and CD = 80 m

Let the point C be at a distance of 'x' m from AB

Angle of elevation to the top of the pole AB to A ∠ACB = 60°

Angle of elevation to the top of the pole DE to E ∠ECD = 30°

From figure,

→ BD = 80 m

→ BC = 'x' m

→ CD = BD - BC = ( 80 - x ) m

Consider ΔABC

tan 60° = Opposite side / Adjacent side

⇒ √3 = AB / BC

[ ∵ tan 60° = √3 ]

⇒ √3 = AB / x

⇒ √3 * x = AB

⇒ x = AB / √3 → eq ( 1 )

Consider ΔCDE

tan 30° = Opposite side / Adjacent side

⇒ 1 / √3 = DE / CD

[ ∵ tan 30° = 1 / √3 ]

⇒ 1 / √3 = DE / ( 80 - x )

⇒ 80 - x = √3 * DE

⇒ 80 - √3 * DE = x

⇒ x = 80 - √3 * DE

⇒ x = 80 - √3 * AB → eq ( 2 )

[ ∵ DE = AB ]

From eq ( 1 ) and eq ( 2 )

⇒ AB / √3 = 80 - √3 * AB

⇒ AB = √3 ( 80 - √3 * AB )

⇒ AB = 80√3 - 3AB

⇒ AB + 3AB = 80√3

⇒ 4AB = 80√3

⇒ AB = 80√3 / 4

⇒ AB = 20√3

⇒ AB = 20 * 1.732

[ ∵ √3 ≈ 1.732 ]

⇒ AB = 34.64

Hence, height of the pole is 34.64 m.

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