[table][br][tr][br][td]Sine Rule[/td][br][td]サインの法則[/td][br][td]사인 법칙[/td][br][td]正弦定理[/td][br][/tr][br][tr][br][td]Triangle[/td][br][td]三角形[/td][br][td]삼각형[/td][br][td]三角形[/td][br][/tr][br][tr][br][td]Solving Triangles[/td][br][td]三角形の解法[/td][br][td]삼각형 풀기[/td][br][td]解三角形[/td][br][/tr][br][tr][br][td]Acute Triangles[/td][br][td]鋭角三角形[/td][br][td]예각 삼각형[/td][br][td]锐角三角形[/td][br][/tr][br][tr][br][td]Obtuse Triangles[/td][br][td]鈍角三角形[/td][br][td]둔각 삼각형[/td][br][td]钝角三角形[/td][br][/tr][br][tr][br][td]Angles[/td][br][td]角度[/td][br][td]각도[/td][br][td]角度[/td][br][/tr][br][tr][br][td]Sides[/td][br][td]辺[/td][br][td]변[/td][br][td]边[/td][br][/tr][br][tr][br][td]Pythagorean Theorem[/td][br][td]ピタゴラスの定理[/td][br][td]피타고라스 정리[/td][br][td]勾股定理[/td][br][/tr][br][tr][br][td]Ambiguous Case[/td][br][td]曖昧な場合[/td][br][td]애매한 경우[/td][br][td]模棱两可的情况[/td][br][/tr][br][tr][br][td]Sum of Angles[/td][br][td]角度の合計[/td][br][td]각의 합[/td][br][td]角度之和[/td][br][/tr][br][/table]

[table][br][tr][br][td][b]Factual Inquiry Questions[/b][br]What is the Sine Rule and how is it formulated for any triangle?[br][br]Under what conditions is the Sine Rule most effectively used in solving triangles?[br][/td][br][br][td][b]Conceptual Inquiry Questions[/b][br]Why is the Sine Rule applicable in both acute and obtuse triangles, and how does it facilitate solving such triangles?[br][br]How does the Sine Rule illustrate the relationship between the angles and sides in a triangle's proportionality?[br][/td][br][br][td][b]Debatable Inquiry Questions[/b][br]In what scenarios is the Sine Rule more advantageous to use over the Cosine Rule, and why?[br][br]Can the Sine Rule be considered a more fundamental geometric principle than the Pythagorean Theorem due to its broader applicability?[br][/td][br][/tr][br][/table][br]

The sine rule states that every triangle has a constant that is calculated by dividing a side length by the sine of its opposite angle. [br][br]That is, that for a triangle with vertices A, B C and sides a, b, c, as in the figure below, the number[br][br][center][math]\frac{a}{sin\left(A\right)}[/math][/center][br]is equal to [br][center][br][math]\frac{b}{sin\left(B\right)}[/math][/center][right][/right]which in turn is equal to [br][br][center][math]\frac{c}{sin\left(C\right)}[/math][/center][left][/left][br]Check this out on the applet below.[br]

Is it possible to create two different triangles that have the same constant?

Part 2 - The ambigious case

See the below video to see more examination style questions

Exam style questions involving sine rule [br]Question. 7, 8, 11, 16, 17, 18, 19