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secondary 2 | Maths
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The Singapore flyer has 28 pods spaced out evenly in a circle. Alex, Blake and Cyndi decide to ride the Singapore flyer. How many possible combinations are there if each of them were to occupy a pod and for them to form the vertices of a right-angled triangle? If they were to occupy the same pods but in different order, it would not count as a different combination.
Date Posted: 3 years ago
Views: 253
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Hi adwin, I'm not a maths god but let me try to help.
So based on the diagram I drew right you can see that there are a total of 28 pods, and because they are evenly divided, pods 1 to 8 will form a quarter circle and pods 1 to 15 will form a semi circle which means there is a 90degree angle will form at pod 8 between pod 1 and 15 (pods 1 and 15 being the semi circle) so here we have our right angled triangle.
So the question now is how many of these triangles can we form.
So imagine the 90 degree point of our triangle is like the hand on a clock, and we want to see how many points it can go until it returns to the original position.
So we count how many points there are and it's 28 and so our answer is 28.
So based on the diagram I drew right you can see that there are a total of 28 pods, and because they are evenly divided, pods 1 to 8 will form a quarter circle and pods 1 to 15 will form a semi circle which means there is a 90degree angle will form at pod 8 between pod 1 and 15 (pods 1 and 15 being the semi circle) so here we have our right angled triangle.
So the question now is how many of these triangles can we form.
So imagine the 90 degree point of our triangle is like the hand on a clock, and we want to see how many points it can go until it returns to the original position.
So we count how many points there are and it's 28 and so our answer is 28.
Date Posted:
3 years ago
Aren't there a lot more pairs of pods that will form the diameter of the flyer? You only looked at 1 and 15. There are other pairs like 2 and 16, 3 and 17, 4 and 18 and so on, for a total of 28 pairs.
Each of these pairs can be paired with any other pods to form a right triangle. Since each of these pairs have 26 possible combinations, wouldn't that make a total of (26 × 28) possible combinations?
Each of these pairs can be paired with any other pods to form a right triangle. Since each of these pairs have 26 possible combinations, wouldn't that make a total of (26 × 28) possible combinations?
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Hi adwin, I'm not a maths god but let me try to help.
So based on the diagram I drew right you can see that there are a total of 28 pods, and because they are evenly divided, pods 1 to 8 will form a quarter circle and pods 1 to 15 will form a semi circle which means there is a 90degree angle will form at pod 8 between pod 1 and 15 (pods 1 and 15 being the semi circle) so here we have our right angled triangle.
So the question now is how many of these triangles can we form.
So imagine the 90 degree point of our triangle is like the hand on a clock, and we want to see how many points it can go until it returns to the original position.
So we count how many points there are and it's 28 and so our answer is 28.
So based on the diagram I drew right you can see that there are a total of 28 pods, and because they are evenly divided, pods 1 to 8 will form a quarter circle and pods 1 to 15 will form a semi circle which means there is a 90degree angle will form at pod 8 between pod 1 and 15 (pods 1 and 15 being the semi circle) so here we have our right angled triangle.
So the question now is how many of these triangles can we form.
So imagine the 90 degree point of our triangle is like the hand on a clock, and we want to see how many points it can go until it returns to the original position.
So we count how many points there are and it's 28 and so our answer is 28.
Date Posted:
3 years ago
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