Question

question 3 of 10
which of the following problem types can always be solved using the law of cosines or sines? check all that apply.
a. asa
b. sas
c. sss
d. saa
e. aaa
f. ssa

Explanation:

• ASA (Angle - Side - Angle): With two angles and the included side, we can find the third angle (since the sum of angles in a triangle is \(180^{\circ}\)) and then use the Law of Sines to find the other sides.
• SAS (Side - Angle - Side): The Law of Cosines can be used to find the third side, and then the Law of Sines can be used to find the other angles.
• SSS (Side - Side - Side): The Law of Cosines can be used to find any of the angles.
• SAA (Side - Angle - Angle): Similar to ASA, we can find the third angle and then use the Law of Sines to find the other sides.
• SSA (Side - Side - Angle): The Law of Sines can be used here, although there may be the ambiguous case (two possible triangles, one triangle, or no triangle), but it can still be solved using the Law of Sines.
• AAA (Angle - Angle - Angle): AAA only gives the similarity of triangles, not the actual side lengths. We need at least one side length to determine the size of the triangle, so we cannot always solve a triangle with just AAA using the Law of Sines or Cosines.

Answer:

A. ASA, B. SAS, C. SSS, D. SAA, F. SSA