Assume triangle ABC has standard labeling and complete the statement below.
(a) Determine whether SAA, ASA, SSA, SAS, or SSS is given.
(b) Decide whether the law of sines or the law of cosines should be used to begin solving the triangle.
Choose the appropriate representation of a, c, and A.
A. SSS
B. SSA
C. ASA
D. SAS
E. SAA

This question is based on the concept of rules of triangle congruency. Therefore, the appropriate representation of a, c, and A is B, i.e. SSA and law of sines.

Given:

Assume triangle ABC has standard labeling. Attachment of figure is below.

We need to decide the law of sines or the law of cosines should be used to begin solving the triangle.

According to the question,

It is given that triangle ABC has standard labeling, then A, B and C are angles, and a is the opposite side to A, b is the opposite side to B and c is the opposite side to C.

If a, c, and A are given, then we have to find a side, another side and an angle. This  would be determined by Side-Side-Angle congruency rule.

By using law of sines states:

In the above expression only unknown is C. Thus, the law of sines should be used to begin solving the triangle.

Therefore, the appropriate representation of a, c, and A is B, i.e. SSA and law of sines.

For further details, please refer this link:

link

SSA, the law of sines

Step-by-step explanation:

Given that triangle ABC has standard labeling, then A, B and C are angles, and a is the opposite side to A, b is the opposite side to B and c is the opposite side to C (see figure attached).

If a, c, and A are given, then we know a side, another side and an angle, that is, SSA.

Law of sines states:

sin(A)/a = sin(C)/c

where the only unknown is C. So, the law of sines should be used to begin solving the triangle

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step-by-step explanation:

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