Two strips of width 1 intersect at an angle α. Find the distance C between the intersection points of strip sides, as shown in the attached drawing.
2026-03-29 10:28:59.1774780139
offsetting lines
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From your drawing, when the "offset" (strip width) is 1, the formula for the length of segment $c$ is $$ c = {1\over\sin{\alpha\over2}} = \csc {\alpha\over2}, $$ where $\alpha$ is the angle formed by the two vectors (so ${\alpha\over2}$ is your "half-angle").
This is due to the fact that $c$ is the hypotenuse of a right triangle that has a leg of length $1$ opposite the angle ${\alpha\over2}$.