Age 16 to 18 Challenge Level:
The challenge here is to visualise the diagram.
You can reason that a symmetrical solution is likely and then
concentrate on the shape that is enclosed by the line segments.
Calculate the angles and lengths in this shape before calculating
the required lengths of the line segments.
You will need some trigonometry. Don't get put off by the
calculation. The solution only requires simple geometry of
right-angled triangles and polygons.