# A circular curve of radius R connects two points of tangent. What is the length of the tangent if the angle of deflection is 30°?

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A circular curve of radius R connects two points of tangent. What is the length of the tangent if the angle of deflection is 30°?
1. 0.115R
2. 0.27R
3. 0.78R
4. 0.58R

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Correct Answer - Option 2 : 0.27R

Explanation:

Tangent length of the curve is given by,

${\rm{T}} = {\rm{R}}\tan \frac{{\rm{Δ }}}{2}{\rm{\;}}$

Where,

Δ = Deviation or deflection angle in degrees

Δ = Deflection angle

R = Radius of curve in m

Calculation:

Given,

Δ = 30°

Tangent length is given by, ${\rm{T}} = {\rm{R}}\tan \frac{{\rm{Δ }}}{2}{\rm{\;}}$

T = R × tan(30°/2) = 0.267R ≈ 0.27R