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 tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
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Location: Bergen
    
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 Posted:
Sun Apr 04, 2010 4:12 am Post subject: brainTeaser[2] (BIG HINT FROM 1) |
 
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The elongation α of a planet is the angle formed by the planet, Earth, and the Sun. When Venus achieves its maximum elongation of 46.3º, the Earth, Venus, and the sun form a triangle with a right angle at Venus. Find the distance between Venus and the sun in Astronomical Units (AU). (By definition, the distance between the Earth and the Sun is 1 AU.)
HINT: LOOK AT THE ANSWER FOR brainTeaser[1] TO GET A SIMILAR ANSWER...
Answer to brainTeaser[1]
| tr1sth3t wrote: |
ANSWER:
V1 and V2 are the positions of Venus, E is the earth and S is the Sun. Since the distance from the Sun to Venus are the same consider SV1 = SV2 = 0.723AU. Consequently, the corresponding opposite angles are equal. So, the remaining angles are measured.
Now, using law of sines we have
[ V2E ÷ sin(xº) ] = [ 1 ÷ sin(140.6 - x)º ] = [ 0.723 ÷ sin(39.4º) ]
⇒ V2E = sin(xº)[ 0.723 ÷ sin(39.4º) ]
also, sin(140.6 - x)º = [ sin(39.4º) ÷ 0.723 ]
⇒ xº = 140.6º - sinˉ¹[ sin(39.4º) ÷ 0.723 ] = 79.208º
∴ V2E = 1.11891 astronomical units.
Again from the triangle V1SV2 , using the sine law we get
[ 0.723 ÷ sin(140.6 - x)º ] = [ V1V2 ÷ sin(101 - 2x)º ]
⇒ V1V2 = -0.708079 AU
∴ V1E = 1.11891-0.708079 = 0.42 AU
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 beladakin
Lieutenant Commander
Joined: Dec 05, 2008
Member#: 6509
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Location: Ankara
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Posted:
Sun Apr 04, 2010 4:24 am Post subject: |
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agreed |
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 SeclusionSolution 
Commodore
Joined: Jun 22, 2006
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Location: Papua New Guinea
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Posted:
Sun Apr 04, 2010 1:03 pm Post subject: |
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voted yes  
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diginferno
Rear Admiral (Ambassador)
Joined: Apr 11, 2006
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Posts: 3182
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Posted:
Sun Apr 04, 2010 1:31 pm Post subject: |
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Why is the rum always gone? 
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diginferno
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 Necrophagist666
Lieutenant Commander
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Joined: Oct 06, 2008
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Location: Under your bed...
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Posted:
Sun Apr 04, 2010 2:42 pm Post subject: |
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Support! 
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tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
Member#: 3130
Posts: 279
Location: Bergen
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Posted:
Sun Apr 04, 2010 3:16 pm Post subject: |
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To which part? 
| SeclusionSolution wrote: |
| voted yes |
What are we voting for?
| diginferno wrote: |
| Why is the rum always gone? |
I don't know. There are some alcoholics around here I think. 
| Necrophagist666 wrote: |
| Support! |
I am thankful, I think.
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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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irule
Captain
Joined: Sep 20, 2006
Member#: 2410
Posts: 1379
Location: Canada
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Posted:
Mon Apr 05, 2010 12:29 am Post subject: |
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I got 0.7229671459095681, however it was very easy to get so I'm most likely wrong...
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 the_Fallen_Chivo
Commander
Joined: Jul 06, 2009
Member#: 8272
Posts: 580
Location: Stalking you right now!!! Don't look behind you!!
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Posted:
Mon Apr 05, 2010 8:33 am Post subject: |
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man i'm too high!!! what where we talkin about again...?  |
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tr1sth3t
Lieutenant Commander
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Location: Bergen
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Posted:
Mon Apr 05, 2010 11:19 am Post subject: |
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| irule wrote: |
| I got 0.7229671459095681, however it was very easy to get so I'm most likely wrong... |
Your answer is precisely correct.
[quote=the_Fallen_Chivo]man i'm too high!!! what where we talkin about again...?[/quote]
The distance between Venus and the Sun. 
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irule
Captain
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Location: Canada
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Posted:
Mon Apr 05, 2010 10:38 pm Post subject: |
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Yay, easy trig with no annoying calculus!  |
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 Dami
Commodore
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Posted:
Wed Apr 07, 2010 11:22 am Post subject: |
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Stop with the fucking math. Makes your head spin just looking at the numbers  .
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tr1sth3t
Lieutenant Commander
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Posted:
Wed Apr 07, 2010 4:47 pm Post subject: |
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| Dami wrote: |
| Stop with the fucking math. Makes your head spin just looking at the numbers . |
That's okay. Your head really is spinning because the Earth is and those are circular functions.
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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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Dami
Commodore
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Location: Stalag 13
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Posted:
Thu Apr 08, 2010 12:11 pm Post subject: |
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Well that sure makes big sense and all but really I suck at math, in school I understood the things when the class tests were done, not before. But hey I'm good at everything with the PC and languages, so who cares?
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irule
Captain
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Location: Canada
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Posted:
Thu Apr 08, 2010 5:03 pm Post subject: |
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It is very easy. I used an online trig calculator for the function sine. The sine ratio of 46.3 degrees is 0.72297. Using the rule SOH (sine = opposite side over hypotenuse), 0.72297 = distance between venus and the sun / 1. So the distance is 0.72297 |
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Necrophagist666
Lieutenant Commander
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Posted:
Thu Apr 08, 2010 6:32 pm Post subject: |
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i really dont care enough to do this.. (a.k.a. i have my own calculus work to do) 
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You should have died when I killed you -John LeCarre
http://soundcloud.com/ethosprophecy |
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