Problem

Assume a triangle ABC has standard labeling. (a) Determine whether SAA, ASA, SSA, SAS, or SSS is given below. (B) decide whether the law of sines or the law of cosines should be used to begin solving the triangle. $A, C$, and $c$ (a) Choose the correct answer below. SAS SSS SSA ASA SAA (b) Choose the correct answer below. A. Law of Sines B. Law of Cosines C. The triangle cannot be solved.

Solution

Step 1 :Given the measures of two angles and one side of a triangle, namely $A$, $C$, and $c$ respectively, we need to identify the type of triangle information given and the appropriate trigonometric law to use for solving the triangle.

Step 2 :The given information corresponds to the ASA (Angle-Side-Angle) configuration, as we have two angles and the side between them.

Step 3 :Since we have the ASA configuration, we can use the Law of Sines to solve the triangle.

Step 4 :Final Answer: \(\boxed{\text{(a) ASA}}\)

Step 5 :Final Answer: \(\boxed{\text{(b) Law of Sines}}\)

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Source: https://solvelyapp.com/problems/19595/

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