What should you use when an angle is enclosed by two given sides?

When dealing with an angle that is enclosed by two given sides, the most relevant relationship to use is the Cosine Rule. The Cosine Rule allows you to find an unknown side or angle in any triangle, particularly when you have two sides and the included angle or when you have all three sides and want to determine an angle.

In this case, since you are given two sides and the included angle is what needs to be calculated or confirmed, the Cosine Rule is particularly suitable. It is expressed as ( c^2 = a^2 + b^2 - 2ab \cos(C) ), where ( C ) is the included angle between sides ( a ) and ( b ), and ( c ) is the side opposite angle ( C ). This effectively helps in relating the lengths of the sides of the triangle to the cosine of the included angle.

Other options do not fit as appropriately for the scenario described. The Pythagorean theorem is useful for right-angled triangles but won't apply if the triangle is not right-angled. The Sine Rule is used for determining unknown lengths or angles where you have an angle opposite a known side, or vice versa, which does not exactly match the situation of having