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Chapter 7: 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
Yes, the statement makes sense. When solving a triangle with Side-Side-Side (SSS), you don't need to worry about the ambiguous case while using the Law of sines because, with three given sides, the triangle is uniquely determined.

Step by step solution

01

Understanding the Problem

The statement mentions about 'solving an SSS triangle' which means we are given the lengths of all three sides of a triangle. And it says 'using the law of sines' - the law of sines is a formula in trigonometry stating that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides and angles in a given triangle.
02

Analyzing the Law of Sines and the Ambiguous Case

The law of sines can be used to find a missing side or a missing angle in a triangle. The ambiguous case happens when, given two sides and an angle, there are two possible triangles. This is usually denoted as Angle-Side-Side (ASS) or Side-Side-Angle (SSA). It is important to mention that there is no ambiguous case for Side-Side-Side (SSS) because with three given sides, only one triangle is possible.
03

Final Judgment

The statement mentioned in the problem seems to make sense. The ambiguous case can occur while using the Law of sines is not a concern when it comes to a Side-Side-Side (SSS) triangle. The statement makes sense because with three given sides, the triangle is uniquely determined, and there is no possibility of an ambiguous case.

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