$$An inclined minor road intersects a four$-$lane divided highway at an angle of $60$ degrees $($instead of a perpendicular intersection$).$ The highway has a speed limit of $55$ mi$/$h$,$ while the minor road has a speed limit of $35$ mi$/$h$.$ The intersection is controlled by a yield sign on the minor road. Determine the dimensions of the triangle formed at the intersection, including the sight distance required for a vehicle on the minor road to cross the intersection safely.

Provide a diagram of the intersection with the following details:

$$ The $60-$degree angle between the minor road and the major road.

$$ Lane width of the major road $=11$ ft$.$

$$ Median width $=8$ ft$.$

$$ Design vehicle length $=22$ ft$.$

$$ Approach grade on the minor road $=3\%.$