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If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection, is
- a)300
- b)600
- c)900
- d)1200
Correct answer is option 'D'. Can you explain this answer?
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If the long chord and tangent length of a circular curve of radiusRare...
Explanation:
Given, long chord and tangent length of a circular curve of radius 'R' are equal to the angle of deflection.
Let us consider a circular curve of radius 'R' as shown below.
https://www.edurev.in/api/download/1328321" />
From the above figure,
Long chord length = AB = 2Rsin(Δ/2)
Tangent length = AC = Rtan(Δ/2)
Where Δ is the angle of deflection.
Given, long chord length = tangent length
=> 2Rsin(Δ/2) = Rtan(Δ/2)
=> 2sin(Δ/2) = tan(Δ/2)
=> 2sin(Δ/2) = sin(Δ/2)/cos(Δ/2)
=> 2cos(Δ/2) = 1
=> cos(Δ/2) = 1/2
=> Δ/2 = 60°
=> Δ = 120°
Therefore, the angle of deflection is 1200.
Hence, the correct option is D) 1200.
Given, long chord and tangent length of a circular curve of radius 'R' are equal to the angle of deflection.
Let us consider a circular curve of radius 'R' as shown below.
From the above figure,
Long chord length = AB = 2Rsin(Δ/2)
Tangent length = AC = Rtan(Δ/2)
Where Δ is the angle of deflection.
Given, long chord length = tangent length
=> 2Rsin(Δ/2) = Rtan(Δ/2)
=> 2sin(Δ/2) = tan(Δ/2)
=> 2sin(Δ/2) = sin(Δ/2)/cos(Δ/2)
=> 2cos(Δ/2) = 1
=> cos(Δ/2) = 1/2
=> Δ/2 = 60°
=> Δ = 120°
Therefore, the angle of deflection is 1200.
Hence, the correct option is D) 1200.
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If the long chord and tangent length of a circular curve of radiusRare equal the angle of deflection, isa)300b)600c)900d)1200Correct answer is option 'D'. Can you explain this answer?
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