Question $3[15$ marks$]$

A sag vertical curve joins $a-2\%$ grade and $a+1\%$ grade. If the point of vertical intersection $($PVI$)$ of the grades is at station $(535+25)$ and has an elevation of $90m,$ determine the station and elevation of the beginning of vertical curve $($BVC$)$ and the end of vertical curve $($EVC$)$ provided that $K=60.$ Figure $Q3$ shows a layout of the curve. In addition, determine the tangent elevation of stations $529+00,$ and $540+00.$