Questions: Which of the following problem types can always be solved using the law of cosines or sines? Check all that apply. A. AAA B. SAA C. SSA D. SAS E. ASA F. SSS

Solution Steps

To determine which problem types can always be solved using the law of cosines or sines, we need to understand the conditions under which these laws are applicable:

1. Law of Sines is applicable in the following cases:

   • Angle-Angle-Side (AAS)
   • Angle-Side-Angle (ASA)
   • Side-Side-Angle (SSA) (with caution due to the ambiguous case)

2. Law of Cosines is applicable in the following cases:

   • Side-Angle-Side (SAS)
   • Side-Side-Side (SSS)

Given these conditions, we can identify which problem types can always be solved using these laws.

To determine which problem types can always be solved using the law of cosines or sines, we need to understand the conditions under which these laws are applicable:

1. Law of Sines is applicable in the following cases:

   • Angle-Angle-Side (AAS)
   • Angle-Side-Angle (ASA)
   • Side-Side-Angle (SSA) (with caution due to the ambiguous case)

2. Law of Cosines is applicable in the following cases:

   • Side-Angle-Side (SAS)
   • Side-Side-Side (SSS)

Based on the conditions identified in Step 1, we evaluate each problem type:

• AAA (Angle-Angle-Angle): Cannot determine the sides, so it cannot be solved using these laws.
• SAA (Side-Angle-Angle): Equivalent to AAS, can be solved using the Law of Sines.
• SSA (Side-Side-Angle): Can be solved using the Law of Sines, but with caution due to the ambiguous case.
• SAS (Side-Angle-Side): Can be solved using the Law of Cosines.
• ASA (Angle-Side-Angle): Can be solved using the Law of Sines.
• SSS (Side-Side-Side): Can be solved using the Law of Cosines.

Final Answer