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
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.
