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Chapter 6: Problem 64

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Solving an SSS triangle, I do not have to be concerned about the ambiguous case when using the Law of sines.

Short Answer

Expert verified
The statement makes sense because in an SSS triangle, we don't have to worry about the ambiguous case of the Law of Sines. Because the triangle is completely defined with all side lengths, there's no ambiguity in solving for the triangle's angles.

Step by step solution

01

- Understanding Triangles and Conditions

First, it's important to recognize that, in an SSS triangle, we know the lengths of all three sides. Therefore, there's no ambiguity about the shape and size of the triangle - it's uniquely determined.
02

- Grasping the Ambiguity of the Law of Sines

Next, remember that the Law of Sines can potentially produce two different angles that satisfy the law, if we are given two sides and one angle (SSA condition). This is called the ambiguous case.
03

- Evaluating the Statement

Taking into consideration the information from steps 1 and 2, we can see that when we have an SSS triangle, we're not faced with the ambiguous case that can occur when using the Law of Sines. Therefore, the statement does make sense. There is no ambiguity on SSS triangles as they are already defined and unique, hence we don鈥檛 have to be concerned about the ambiguous case of the Law of Sines.

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