A horizontal curve has a deflection angle $1=20\backslash$deg $18*02"$ and a degree of curvature $400\text{'}.$ The point of intersection $($PI$)$ is $5+053\mathrm{.}87($km $+$ m$).$ Compute the following:$(1)$ The radius, R $(4$ marks$)(*)$ The tangent length, T $(2$ marks$)($i$)$ External distance E $(2$ marks$)($iv$)$ Curve length, L $(2$ marks$)($v$)$ Chainages for the points of curvature $($PC$)$ and tangency $($PT$).(3$ marks$)$The degree of curve is defined as an angle that subtends an are length of $20$m $($Ministry of Works definition$).$