posted
Help me with this -- I know it's terribly easy, but I'm blanking on it. The State Fair is running, and I've thought of doing a day there with a friend, which may explain why I dreamed about it.
In my dream, I could see the biggest Ferris wheel on the midway from my home. In fact, it extended about 45° up into the sky.
The Fairgrounds are about twenty miles from here.
How big would the Ferris wheel have to be? Discount the curvature of the earth, if that makes it easier.
-------------------- “Just because your voice reaches halfway around the world doesn't mean you are wiser than when it reached only to the end of the bar.” -- Edward R. Murrow
posted
Well, let's see: You would have a right triangle, with the Ferris wheel as the side opposite the hypotenuse and the ground as a base.
Say the top of the Ferris wheel is point A. Your house is point B. The base of the Ferris wheel is Point C.
The angle at the base of the Ferris wheel is 90 degrees. The angle at the top of the Ferris wheel is 45 degrees (because that's what you said it appeared to be). Therefore, logically, the last angle would be 45 degrees as well (the sum of all the angles of any triangle is 180 degrees).
Line BC is 20 miles. You want to find the distance of the line AC.
I get seventy-nine kajiggerbazillion miles.
-------------------- "No hard feelin's and HOPpy New Year!"--Walt Kelly Hear what you're missing: ARTC podcasts! http://artcpodcast.org/ Posts: 7581 | From: Gainesville, Georgia | Registered: Jun 2000
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Opposite is the height of the ferris wheel. Adjacent is the distance to it.
So sin 45 degrees = height/20 miles.
therefore height = sin (45 degrees)*20
=0.707*20
Or just over 14 miles.
-------------------- "Ladies and gentlemen, this is what is commonly known as money. It comes in all sizes, colours, and denominations - like people." Posts: 997 | From: Maidstone, UK | Registered: Jun 2006
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posted
If it's a 45° angle then the two perpendicular sides of the triangle (distance between your house and the wheel, height of the wheel) are equal, therefore the Ferris wheel is 20 miles high.
posted
Thank you all. (One way or another it comes out "higher than is practical for Ferris wheel construction".)
-------------------- “Just because your voice reaches halfway around the world doesn't mean you are wiser than when it reached only to the end of the bar.” -- Edward R. Murrow
posted
Bugger. It's the tangent not the sine. Which is tan 45 * 20
Or 1 * 20
Em Wins.
-------------------- "Ladies and gentlemen, this is what is commonly known as money. It comes in all sizes, colours, and denominations - like people." Posts: 997 | From: Maidstone, UK | Registered: Jun 2006
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posted
[hijack]I clicked on this because I loved the title of the thread: "geometry from a dream." Beautiful. I just may steal it if I ever get the urge to do a surrealist painting. Or start an emo band. [/hijack]
-------------------- saxea ut effigies bacchantis prospicit eheu | prospicit et magnis curarum fluctuat undis -Catullus Posts: 435 | From: Iowa | Registered: Mar 2006
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(And now I'm trying to picture a twenty-mile Ferris wheel. That's 3.6 times the height of Everest. There's be a hell of a view, though.)
-------------------- “Just because your voice reaches halfway around the world doesn't mean you are wiser than when it reached only to the end of the bar.” -- Edward R. Murrow
posted
If you want to take the curvature of the Earth into account, then assuming that the Earth's average radius is 3959 miles, and using the law of sines:
sin A / a = sin B / b = sin C / c,
I have determined that your Ferris Wheel would actually be 20.12 miles tall.Posts: 306 | From: Tacoma, WA | Registered: Sep 2005
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quote:Originally posted by beaver_slayer: Lord, this is a problem for 7-grader
Particularly if we strap the 7th grader into a car on our 20 mile high ferris wheel.
-------------------- "Ladies and gentlemen, this is what is commonly known as money. It comes in all sizes, colours, and denominations - like people." Posts: 997 | From: Maidstone, UK | Registered: Jun 2006
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posted
Hmm, have any of you considered the effect of the field of human vision? (If you see in first person in your dreams, I see in first person in my dreams) Lens, focal length, and field of vision affects how we perceive distance and size and none of your trig calculations have taken this into account. Really, we need more information than just "45 degrees" to make any well informed guesses. There is "math vision" of distance and size, and then there is our eye's vision.
-------------------- Obi Wan: "Only a Sith deals in absolutes!" Anakin: "Um, isn't your last statement an absolute?" Posts: 166 | From: San Antonio, Texas | Registered: Sep 2006
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posted
Isn't this one o' them trigger-nometry questions, anyhoo?
I was never that good a shot.
-------------------- "No hard feelin's and HOPpy New Year!"--Walt Kelly Hear what you're missing: ARTC podcasts! http://artcpodcast.org/ Posts: 7581 | From: Gainesville, Georgia | Registered: Jun 2000
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posted
I have yet another answer. If the angle is 45 degress, wouldn't he height of the ferris wheel be exactly the distance from your house, or 20 miles?
The distance from your house to the top of the ferris wheel would be 28.28 miles though.
quote:Originally posted by BeachLife: I have yet another answer. If the angle is 45 degress, wouldn't he height of the ferris wheel be exactly the distance from your house, or 20 miles?
The distance from your house to the top of the ferris wheel would be 28.28 miles though.
Erm....yeah, But that's not another answer. Em has answered the same but used trig to prove it. I think Brad's post may have confused people. I'm not sure on the whole seriousness of it because of the use of the word 'kajiggerbazillion', but there is no side opposite a hypotenuse. The 'opposite' in question is the side opposite the angle other than the 90° that you know. Adjacent is the side adjacent to the same angle.
quote:Originally posted by BeachLife: I have yet another answer. If the angle is 45 degress, wouldn't he height of the ferris wheel be exactly the distance from your house, or 20 miles?
The distance from your house to the top of the ferris wheel would be 28.28 miles though.
Erm....yeah, But that's not another answer. Em has answered the same but used trig to prove it. I think Brad's post may have confused people. I'm not sure on the whole seriousness of it because of the use of the word 'kajiggerbazillion', but there is no side opposite a hypotenuse. The 'opposite' in question is the side opposite the angle other than the 90° that you know. Adjacent is the side adjacent to the same angle.
When showing your work, using two different methods to get to the same result, is two different answers.
quote:Originally posted by Em: Is it a BYO oxygen deal, or is that supplied?
You'd better have a pressure suit.
And it had better have built-in restroom facilities. If this Ferris Wheel has a car ever 100 ft, there would be 3318 cars on it. Assuming you could load and unload a car in 30 seconds, it would take 28 hours for a single pass around the Ferris Wheel. If you used some automated loading/unloading system, you could shorten the trip time to 1 hour, but you'd be traveling 62 mph laterally, so you'd have to load/unload without stopping the wheel.
PS. I think a 20 mile high Ferris Wheel would be a heck of a navigation hazard for aircraft.
-------------------- IIRC, it wasn't the shoe bomber's loud prayers that sparked the takedown by the other passengers; it was that he was trying to light his shoe on fire. Very, very different. Canuckistan Posts: 3694 | From: Arizona | Registered: Aug 2005
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quote:Originally posted by stalker: I think Brad's post may have confused people. ...
Then my sinister purpose was achieved.
Although I got good grades in math at school, today I'm practically innumerant. My wife won't even let me balance the checkbook...or have any money, for that matter.
-------------------- "No hard feelin's and HOPpy New Year!"--Walt Kelly Hear what you're missing: ARTC podcasts! http://artcpodcast.org/ Posts: 7581 | From: Gainesville, Georgia | Registered: Jun 2000
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