In designing a vertical curve joining a $-2\mathrm{.}00\%$ grade to a $+0\mathrm{.}50\%$ grade on a county

road in Ontario, the centreline of the road must clear an overhead structure located

at station $99+20$ by $5\mathrm{.}67$ m$.$ The elevation of the bottom of the structure is $77\mathrm{.}45$ m

above sea level. What is the maximum length of the curve that can be used, if the

PVI is at station $100+00$ and elevation $69\mathrm{.}50$ m above sea level.

What is the headlight sight distance available on this curve?