Using the Cosine Rule: When Do You Get 2 Answers?

In summary, the conversation discusses the use of the cosine rule and how it can result in two answers, also known as the "Ambiguous case". The speaker is unsure about when this occurs and asks for clarification. Another person mistakenly mentions the sin rule, but it is corrected that it is indeed the cosine rule. The conversation ends with the speaker expressing gratitude for the information.
  • #1
thomas49th
655
0
Hi, I recall that when you use the cosine rule you can sometimes come out with 2 answers (somthing to do with cos graph?). I can't qutie remeber and I've looked through my books and I can't find it. I can use the rule to calculate one side or angle, but when do you get 2 answers? Can someone please explain.

Thankyou
:)
 
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  • #2
I think its called the "Ambiguous case". Not 100% sure though.
 
  • #3
Thanks but I just checked and that's with sin rule :(
 
  • #4
Oh ok, my mistake then. Guess it was worth a shot anyway :P
 
  • #5
you're actually right, I made the mistake thinking it was with cosine! I accidently came across an webpage a few miutes ago when searching for some other maths stuff. It was a good guess

Cheerz
:tongue:
 

1. How is the cosine rule used to find two answers?

The cosine rule, also known as the law of cosines, is used to find the length of a side or the measure of an angle in a triangle. It can be used when two sides and the included angle are known, or when all three sides are known. In the case of finding two answers, it is used when the given information can form two different triangles with different solutions.

2. When do you get two answers when using the cosine rule?

You get two answers when using the cosine rule when the given information can form two different triangles with different solutions. This occurs when the given sides and angles can be arranged in more than one way to form a triangle. In this case, the law of cosines will give two different solutions for the same problem.

3. Can you explain the concept of ambiguous case in the cosine rule?

The ambiguous case in the cosine rule occurs when the given information can form two different triangles with different solutions. This means that the given sides and angles can be arranged in more than one way to form a triangle. In this case, the law of cosines will give two different solutions for the same problem. It is important to carefully consider which solution is the correct one based on the context of the problem.

4. How do you know which solution to use when using the cosine rule?

When using the cosine rule, it is important to carefully consider which solution to use based on the context of the problem. This can often be determined by looking at the given information and considering which solution makes the most sense. For example, if the given angle is acute, then the smaller solution will likely be the correct one. If the given angle is obtuse, then the larger solution will likely be the correct one.

5. Are there any other methods to solve for the ambiguous case in the cosine rule?

Yes, there are other methods to solve for the ambiguous case in the cosine rule. One method is to draw a diagram and carefully label all given information. Then, use the law of sines to solve for the other angle and determine which solution is the correct one. Another method is to use the sine rule to solve for the other angle and use the sum of angles in a triangle (180 degrees) to determine which solution is the correct one. It is important to note that these methods may not always work and it is best to carefully consider the given information and context of the problem.

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