# The tangent distance of a curve of radius 'r' deflected through an angle of 60 degrees will be: ______.

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The tangent distance of a curve of radius 'r' deflected through an angle of 60 degrees will be: ______.
1. r
2. r√3
3. r/√3
4. Infinite

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Correct Answer - Option 3 : r/√3

Concept:

The 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 = 180° - Angle of intersection

R = Radius of curve in m

Calculation:

Given,

R = r, Δ = 60°

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

${\rm{T}} = {\rm{r}} \times \tan \frac{{\rm{60 }}}{2}{\rm{\;}}$

${\rm{T}} = {\rm{r}} \times \tan {{\rm{30 }}}{}{\rm{\;}}$

${\rm{T}} = {\rm{}}\frac{{\rm{r }}}{\sqrt3}{\rm{\;}}$