Question

question 18 of 20
which of the following problem types can always be solved using the law of cosines or sines? check all that apply.
a. sas
b. asa
c. aaa
d. ssa
e. saa
f. sss

Explanation:

• SAS: Two sides and included angle are known. Law of Cosines first finds the third side, then Law of Sines/Cosines finds remaining angles.
• ASA: Two angles and included side are known. First find the third angle, then Law of Sines finds the other sides.
• AAA: Only angles are known; this defines similar triangles, not a unique triangle, so no unique solution exists.
• SSA: This is the ambiguous case; it can have 0, 1, or 2 valid triangles, so it cannot always be solved.
• SAA: Two angles and a non-included side are known. First find the third angle, then Law of Sines finds the other sides.
• SSS: All three sides are known. Law of Cosines can find all angles.

Answer:

A. SAS
B. ASA
E. SAA
F. SSS