The Cosine Rule

Keywords

Cosine Rule	코사인 법칙	余弦定理	余弦定理
Pythagorean Theorem	피타고라스 정리	피타고라스의 정리	勾股定理
Triangle types	삼각형 유형	삼각형의 유형	三角形类型
Sides and angles relationship	변과 각의 관계	변과 각의 관계	边与角的关系
Angle determination	각도 결정	각도 결정	角度确定
Sine Rule	사인 법칙	사인 법칙	正弦定理

Inquiry questions

Factual Inquiry Questions

Conceptual Inquiry Questions

Debatable Inquiry Questions

What is the formula of the Cosine Rule and in which type of triangle can it be applied?

Why does the Cosine Rule work for any type of triangle, and what does it tell us about the relationship between the sides and angles of a triangle?

Is the Cosine Rule more valuable in practical applications than the Sine Rule?

How does the Cosine Rule relate to the Pythagorean Theorem?

How can the Cosine Rule be used to determine the size of an angle given the lengths of all three sides of a triangle?

How does the understanding of the Cosine Rule impact the development of technology, especially in fields requiring precise measurements and calculations?

Could the principles of the Cosine Rule be applied to non-Euclidean geometries, and what would be the implications?

Trigonometry Cosine Rule - find a side

Cosine rule - Finding a missing angle

Checking for understanding

Question 1 In triangle ABC, side a = 7 cm, side b = 24 cm, and side c = 25 cm. What is the measure of angle C?

D)

C)

B)

A)

Question 2 Using the cosine rule, how can you find the length of a side in a triangle if you know two sides and the angle between them?

A)

B)

C)

D)

Question 3 In a triangle with sides of lengths

,

, and the angle

between them, what is the length of side

?

B) 19 cm C) 21 cm D) 17 cm A) 23 cm

Question 4 If in a triangle, side a = 5 cm, side b = 12 cm, and the angle C = 90^\circ\ between them, what is the length of side c ?

B) 11 cm A) 10 cm C) 13 cm D) 14 cm

Question 5 Which statement is true regarding the application of the cosine rule?

B) It is used to find the lengths of sides in polygons. A) It can only be used in right-angled triangles. D) It provides the relationship between the sides and angles of a square. C) It applies to any triangle to relate the sides and angles.

Exam style questions involving cosine rule Question 6, 11, 12, 14, Question 40. leads you to proving the cosine rule.

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES

[MAA 3.1-3.3] 3D GEOMETRY - TRIANGLES_solutions

Optional extension

Proof of cosine rule will not be examined but it can be wonderful to be able to prove the theorems.