The idomatic phrase "at length" means over a period of time, or finally, eventually.
The opposite could be then, immediately, or right away.
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Width would be the "opposite" of length (they are perpendicular dimensions). The opposite status of length (unspecified dimension or time) could be shortness or brevity.
In parallelogram each two opposite sides are parallel and equal in length
The length and width of a rectangle is the same as the length and width of the opposite sides.
the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c
The length of the side opposite the 60° angle is about 14.72(sin 60°) = 0.866The length of the side opposite the 30° angle is 8.5(sin 30°) = 0.5