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°
\({\rm{T}} = {\rm{R}}\tan \frac{{\rm{Δ }}}{2}{\rm{\;}}\)
\({\rm{T}} = {\rm{r}} \times \tan \frac{{\rm{60 }}}{2}{\rm{\;}}\)
\({\rm{T}} = {\rm{r}} \times \tan {{\rm{30 }}}{}{\rm{\;}}\)
\({\rm{T}} = {\rm{}}\frac{{\rm{r }}}{\sqrt3}{\rm{\;}}\)