Twenty two poles were fixed around a circular fish pond. Find the diameter of the pond if the interval between the poles was 6 metres
So I am imagining a 20 sided polygon, where each side is 6 metres,
each central angle of the 20 triangles I can form is 18°
take one of those and construct an altitude to form a right angled triangle.
The hypotenuse of such a right-angled triangle will be the radius of the pond, call it r,
and the angle at the centre will be 1/2 of the 18°, or 9°.
sin 9° = 3/r
r = 3/sin9° = 19.177
so the diameter would be 38.355 metres