Questions: 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, b, and C (a) Choose the correct answer below. SAS SSS SSA ASA SAA

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, b, and C (a) Choose the correct answer below. SAS SSS SSA ASA SAA
Transcript text: 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. $a, b$, and $C$ (a) Choose the correct answer below. SAS SSS SSA ASA SAA
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Solution

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Solution Steps

Step 1: Identify the Given Information

In the problem, we are given two sides \(a\) and \(b\), and one angle \(C\). We need to determine which type of triangle information is provided: SAA, ASA, SSA, SAS, or SSS.

Step 2: Determine the Type of Triangle Information

The given information consists of two sides and a non-included angle. This corresponds to the SSA (Side-Side-Angle) case.

Step 3: Decide the Appropriate Law to Use

For the SSA case, the Law of Sines is typically used to begin solving the triangle. This is because we have an angle and its opposite side, which allows us to set up a proportion using the Law of Sines.

Final Answer

(a) \(\boxed{\text{SSA}}\)

(b) \(\boxed{\text{Law of Sines}}\)

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