Asked by Lazia
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
Answers
Answered by
mathhelper
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
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
Answered by
oobleck
close, but imagine a 22-sided olygon
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.