The document discusses using the rule of cosine to solve for unknown sides of a triangle when certain information is given, such as: - Two angles and one side - Two sides and the angle opposite one of the sides It provides the formulas for the rule of cosine to solve for an unknown side given certain known values. It also includes two example problems applying the rule of cosine to find unknown side lengths of triangles.

1. The Rules of
Cosine

2. Do you remember
about When do we
use the rules of
sine?

3. The rule of sine can be used if :
• Two angles and any length of side are given.
• Two sides and one angle in opposite side are
given.

4. Look at the triangle of ACD :
𝐴𝐷
cos 𝐴 = A𝐷 = 𝑏 cos 𝐴
𝑏
C ℎ = 𝑏 2 − 𝐴𝐷2
2
a = 𝑏 2 − 𝑏 cos 𝐴2
= 𝑏 2 −𝑏 2 𝑐𝑜𝑠 2 𝐴 …. (1)
b h
𝐵𝐷2 = (𝑐 − 𝐴𝐷)2 B
D = 𝑐 2 − 2𝑐𝑏 cos 𝐴 + 𝑏 2 𝑐𝑜𝑠 2 𝐴 …(2)
A
𝑎2 = 𝐵𝐷2 + ℎ2
= (𝑏 2 −𝑏 2 𝑐𝑜𝑠 2 𝐴) + (𝑐 2 − 2𝑐𝑏 cos 𝐴 + 𝑏 2 𝑐𝑜𝑠 2 𝐴)
= 𝑏 2 + 𝑐 2 − 2𝑐𝑏 cos 𝐴

5. By the same way, we get :
• 𝑏 2 = 𝑎2 + 𝑐 2 − 2𝑎𝑐 cos 𝐵
𝑐 2 = 𝑎2 + 𝑏 2 − 2𝑎𝑏 cos 𝐶

6. Activities Class
1. Look at the triangle below!
A
B C
If the length of BC = 3 cm, AC = 6 cm, and the angle of A
is 300. Find the length of AB !
2. From the triangle ABC, a = 2 cm, b = 2 3 cm, and the
angle of A is 300. The length of c is …………………..