Google Classroom
GeoGebraGeoGebra Classroom
GeoGebra

The Sine Rule

Author:Cliff Packman, Lee W Fisher, DavidA

Keywords

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

Inquiry questions

Factual Inquiry Questions What is the Sine Rule and how is it formulated for any triangle? Under what conditions is the Sine Rule most effectively used in solving triangles? Conceptual Inquiry Questions Why is the Sine Rule applicable in both acute and obtuse triangles, and how does it facilitate solving such triangles? How does the Sine Rule illustrate the relationship between the angles and sides in a triangle's proportionality? Debatable Inquiry Questions In what scenarios is the Sine Rule more advantageous to use over the Cosine Rule, and why? Can the Sine Rule be considered a more fundamental geometric principle than the Pythagorean Theorem due to its broader applicability?
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. That is, that for a triangle with vertices A, B C and sides a, b, c, as in the figure below, the number

is equal to



which in turn is equal to



Check this out on the applet below.
Is it possible to create two different triangles that have the same constant?
Part 2 - The ambigious case

What is the significant about the sum of the two possible angles in the ambigious case?

Part 2 - Checking your understanding

See the below video to see more examination style questions

Question 1: In triangle ABC, side a = 8 cm, angle A = 30°, and angle B = 45°. What is the length of side b?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Question 2: Using the sine rule, how can you find the measure of an angle in a triangle if you know two sides and an angle?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Question 3: In a triangle with sides of lengths 7 cm, 24 cm, and 25 cm, what is the sine of the angle opposite the longest side?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)
Exam style questions involving sine rule Question. 7, 8, 11, 16, 17, 18, 19

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES.pdf

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES.pdf

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES_solutions

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES_solutions.pdf

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES_solutions.pdf

Optional extension: Proof of sine rule

Lesson plan - Navigating the Sine Rule in DP Mathematics

Navigating the Sine Rule in DP Mathematics.pdf

Navigating the Sine Rule in DP Mathematics.pdf

The Sine Rule- Intuition pump (thought experiments and analogies)

The Sine Rule.pdf

The Sine Rule.pdf

New Resources

Discover Resources

Discover Topics