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The lengths of long chord and tangents of a circular curve are equal for a deflection angle of
- a)30°
- b)60°
- c)90°
- d)120°
Correct answer is option 'D'. Can you explain this answer?
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The lengths of long chord and tangents of a circular curve are equal f...
The length of long chord (L) = 2RsinΔ/2 and the
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The lengths of long chord and tangents of a circular curve are equal f...
For a deflection angle of 30 degrees, the relationship between the length of the long chord (LC) and the length of the tangent (T) is given by:
LC = T x tan(15°)
This can be derived using the formula for the length of the long chord:
LC = 2 x R x sin(θ/2)
where R is the radius of the circle and θ is the deflection angle.
Similarly, the length of the tangent for a deflection angle of 30 degrees is given by:
T = R x tan(15°)
Therefore, if LC = T, we can substitute the above equations to get:
2 x R x sin(θ/2) = R x tan(15°) x tan(15°)
Simplifying this equation, we get:
2 x sin(θ/2) = tan(15°) x tan(15°)
Using a calculator, we can find that tan(15°) = 0.26795.
Substituting this value, we get:
2 x sin(θ/2) = 0.26795 x 0.26795
Solving for θ, we get:
θ = 2 x arcsin(0.26795/2)
Using a calculator, we can find that θ is approximately 29.07 degrees.
Therefore, for a deflection angle of approximately 29.07 degrees, the lengths of the long chord and tangents of a circular curve are equal.
LC = T x tan(15°)
This can be derived using the formula for the length of the long chord:
LC = 2 x R x sin(θ/2)
where R is the radius of the circle and θ is the deflection angle.
Similarly, the length of the tangent for a deflection angle of 30 degrees is given by:
T = R x tan(15°)
Therefore, if LC = T, we can substitute the above equations to get:
2 x R x sin(θ/2) = R x tan(15°) x tan(15°)
Simplifying this equation, we get:
2 x sin(θ/2) = tan(15°) x tan(15°)
Using a calculator, we can find that tan(15°) = 0.26795.
Substituting this value, we get:
2 x sin(θ/2) = 0.26795 x 0.26795
Solving for θ, we get:
θ = 2 x arcsin(0.26795/2)
Using a calculator, we can find that θ is approximately 29.07 degrees.
Therefore, for a deflection angle of approximately 29.07 degrees, the lengths of the long chord and tangents of a circular curve are equal.
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The lengths of long chord and tangents of a circular curve are equal for a deflection angle ofa)30°b)60°c)90°d)120°Correct answer is option 'D'. Can you explain this answer?
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