Question

When the branches of a compass form an angle of `60^@` the distance between its tips is `8cm.`. Will such a compass go into a box whose longest diagonal is `8cm.`?

Answer 1

No, as compass has a handle at the top and has some width too, it may need a larger box.

Explanation:

It is apparent that when the branches of a compass form an angle of `60^@`, as the branches are of equal lengths, they form an equilateral triangle ,

and as the distance between their tips is `8cm.` (as it forms a circle of radius `8cm`),

its two arms too would be `8cm.`

and hence theoritically this compass can go into a rectangular `8 cm` diagonal box. However, not only compass has its handle at the top, when folded the compass also has some width, so depending on its width and size of its handle, it may need a larger box.