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Trig Help
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Subb Offline
Music Nerd

Posts: 1,466
Joined: Nov 2012
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Given 317 thank(s) in 184 post(s)
Post: #1
Trig Help

So, I'm learning about the law of sine, and this is one of the problems I have to do. I can't get teacher help for it, so I may as well ask you guys. I want to know how to do it.

"Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?"

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Fulltime Member, 2013-2014

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(This post was last modified: 05-08-2014 04:47 AM by Subb.)
05-08-2014 01:30 AM
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no Offline
True Scotsman

Posts: 1,238
Joined: Nov 2012
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Post: #2
RE: Trig Help

I can do this more easily without the law of sines, primarily because I don't remember it. Unfortunately, the program I was writing my explanation in crashed and I am too lazy to rewrite it.

HOWEVER, you will find that if the 24-foot fence is the one making the 75° angle, it will be impossible to form a full triangle. So only one configuration is possible.

Hello, traveler.

This is an ancient account I have not used in a long time. My views have changed much in the intervening months and years.

Nonetheless, I refuse to clean it up. Pretending that I've held my current views since the beginning of time is what we in the industry call a lie. Asking people to do so contributes to moralistic self-loathing. "See, those people have nothing damning! I do! I'm truly vile!"

Because you can never be a good person with a single blemish on the moral record, I thought that simply entertaining some thoughts made me irredeemable. Though I don't care for his writing style, William Faulkner presents a good counterexample. He went from being a typical Southern racist to supporting the civil rights movement. These days we'd yell at him for that, probably.

People are allowed to change their views.

Nevertheless, this period of my life has informed some of how I am today. In good ways and bad ways. To purge it would be to do a disservice to history. Perhaps it will not make anyone sympathetic, but it may help someone understand.

If, after reading all this, you still decide to use the post above as evidence that I am evil today, ask yourself if you have never disagreed with the moral code you now follow. In all likelihood you did, at some point. If some questions are verboten, and the answer is "how dare you ask that," don't expect your ideological opponents to ever change their minds.
05-08-2014 05:54 AM
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Ky Offline
Shadow

Posts: 5,201
Joined: Aug 2012
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Post: #3
Trig Help

Let's assume there are three sides to a triangle: a, b, and c
Opposite each side is an angle: A, B, and C, respectively

The law of sines is as follows:
a/sin(A) = b/sin(B) = c/sin(C)

There are two different ways to plug in your problem if we assume the barn side (and angle opposite) is c:
20/sin(75) = 24/sin(B) = c/sin(C), or
20/sin(A) = 24/sin(75) = c/sin(C)

Uh oh. Looks like we've run into ambiguous case; you may remember the unsolvable SSA (or ASS, hehe) from geometry, and that's what this is. To a triangle like this, there may either be zero, one, or two solutions, depending on the information given.

EDIT: Look up Law of Sines, Ambiguous Case. It's complicated at first, indeed, but you'll master it once you get the hang of it.

Public Service Announcement: First world problems are still problems.
(This post was last modified: 05-08-2014 08:55 AM by Ky.)
05-08-2014 08:24 AM
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thewake Offline
Unconstructive

Posts: 5,917
Joined: Jun 2007
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Post: #4
Trig Help

Calculus is easier than trigonometry. I'm in calculus and I have a vague grasp of trig.

[Image: nAOqYk7.png]

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05-08-2014 12:51 PM
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Ky Offline
Shadow

Posts: 5,201
Joined: Aug 2012
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Given 1469 thank(s) in 972 post(s)
Post: #5
Trig Help

I'm the opposite; I've found most trigonometry to be far easier than calculus, though I'll admit that finding limits is significantly better than solving ambiguous case. (I'm better with the law of cosines anyway)

Public Service Announcement: First world problems are still problems.
05-09-2014 03:49 AM
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no Offline
True Scotsman

Posts: 1,238
Joined: Nov 2012
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Given 474 thank(s) in 299 post(s)
Post: #6
RE: Trig Help

Whoops, you're right. I'm an idiot.

Hello, traveler.

This is an ancient account I have not used in a long time. My views have changed much in the intervening months and years.

Nonetheless, I refuse to clean it up. Pretending that I've held my current views since the beginning of time is what we in the industry call a lie. Asking people to do so contributes to moralistic self-loathing. "See, those people have nothing damning! I do! I'm truly vile!"

Because you can never be a good person with a single blemish on the moral record, I thought that simply entertaining some thoughts made me irredeemable. Though I don't care for his writing style, William Faulkner presents a good counterexample. He went from being a typical Southern racist to supporting the civil rights movement. These days we'd yell at him for that, probably.

People are allowed to change their views.

Nevertheless, this period of my life has informed some of how I am today. In good ways and bad ways. To purge it would be to do a disservice to history. Perhaps it will not make anyone sympathetic, but it may help someone understand.

If, after reading all this, you still decide to use the post above as evidence that I am evil today, ask yourself if you have never disagreed with the moral code you now follow. In all likelihood you did, at some point. If some questions are verboten, and the answer is "how dare you ask that," don't expect your ideological opponents to ever change their minds.
05-09-2014 06:42 AM
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