Which of these problem types cannot be solved using the law of sines
aas
asa
sas
sss

The correct option are B, C and D.

Explanation:

The law of sine states that,

Where A, B, C are interior angles of the triangle and a, b, c are sides opposite sides of these angles respectively as shown in below figure. Only AAS or SSA types problems can be solved by using Law of sine.

Since we need the combination of two sides and one angle or two angles and one side.

In option A, the two consecutive angles are known and a side which makes the second angle with base side is known, therefore the first angle is opposite to the given side, so the law of sine can be used for AAS problems.

Therefore, option A is incorrect.

In option B a side is known and two inclined angle on that line are known. But to use Law of sine we want the line and angle which in not inclined on that line, therefore the ASA problem can not be solved by Law of sine and the option B is correct.

In option C two sides and their inclined angle is known. But to use Law of sine we want the side and angle which in not inclined on that line, therefore the SAS problem can not be solved by Law of sine and the option C is correct.

In  option D three sides are given but any angle is not given, therefore the SSS problem can not be solved by Law of sine and the option D is correct.