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Age 16 to 18 Challenge Level:

Branches of corridor, widths a and b, stick at angle theta.

A long stick has to be carried horizontally along a narrow corridor and around a right-angled bend. The corridor is $a$ centimetres wide on one side of the bend and $b$ centimetres wide on the other side. Find, in terms of $a$ and $b$, the length of the longest stick that can be manoeuvered horizontally around the bend?

If the object is $2$ metres long and the two branches of the corridor are $65$ centimetres and $75$ centimetres respectively is it possible to manoeuvre the stick around the bend?