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Trig Help - Subb - 05-08-2014 01:30 AM

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?"

RE: Trig Help - no - 05-08-2014 05:54 AM

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.

Trig Help - Ky - 05-08-2014 08:24 AM

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.

Trig Help - thewake - 05-08-2014 12:51 PM

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

Trig Help - Ky - 05-09-2014 03:49 AM

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)

RE: Trig Help - no - 05-09-2014 06:42 AM

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