Which rule is applicable for solving non-right-angled triangles?

The Sine Rule is indeed applicable for solving non-right-angled triangles, and its usefulness is particularly prominent in situations where you have either two angles and one side, or two sides and a non-included angle. The Sine Rule states that the ratio of a side length to the sine of its opposite angle is constant for all three sides and angles in a triangle. This makes it highly effective for determining unknown lengths or angles in triangles that do not contain a right angle.

While the Cosine Rule also applies to non-right-angled triangles and is used for finding missing sides or angles when you have two sides and the included angle or all three sides, the Sine Rule is often the preferred method when certain conditions about the angles are met.

The Pythagorean Theorem is not applicable to non-right-angled triangles, as it specifically involves the sides of right-angled triangles. Similarly, the Angle Sum Property, which pertains to the sum of angles in a triangle always equalling 180 degrees, does not directly help in finding unknown lengths or angles of non-right triangles. Therefore, the Sine Rule stands out as the most relevant and effective method for the specified type of triangle.