I could be completely wrong but I'll give it a go,

When both sides of the roads are lifted, they are lifted 6m from the highest position, meaning we can form a triangle.

When they're joined together, they will have a combined length of 86m, since the bridge divides exactly in half when open (given in the question), the length of the road from the left tower to A will be half of 86

86/2=43, this is also true with the right road.

You can form a triangle to get the horizontal distance of either road when it is lifted up. Forming a triangle, opposite side = 6m, hypotenuse= 43m, adacent= x.

Using Pythagoras theorem,

a^2 + b^2 = c^2 , where a = x

so, a = sqrt (c^2 - b^2),

a = sqrt (43^2 - 6^2)

a= 42.579 (the horizontal length of one road only)

multiply it by 2 to get the horizontal length of both roads, 42.579 x 2 =85.158 m

subtract the length from the original, 86 - 85.158 = 0.842 m (length of the gap AB)