Question

Which of these problem types can not be solved using the Law of Sines?

Answer 1

A. sss because we need an angle to solve using law of sines

Answer 2

Answer: The correct option are A, B and D.

Explanation:

The law of sine states that,

$\frac{\sin A}{a} =\frac{\sin B}{b}=\frac{\sin C}{c}$

Where A, B, C are interior angles of the triangle and a, b, c are sides opposite these angles respectively as shown in below figure.

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

The Law of sine is useful for AAS and SSA type problems.

Reason for correct option:

In  option A three sides are known but no angle is not given, therefore the SSS problem can not be solved by Law of sine and the option A is correct.

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 D 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 D is correct.

Reason for incorrect option:

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

Therefore, option C is incorrect.