sine and cosine Rules

Sine Rule

Example

In triangle ABC, <A = 50° , a = 8 cm , b = 6 cm. Find <B, <C, Side c

Cosine Rule

Example

In triangle ABC, <C = 40°, a = 8 cm , b = 6 cm. Find c.

c² = a² + b² – 2ab Cos C

c² = 8² + 6² – 2 (8) (6) Cos 40°

c² = 64 + 36 – 73.54

c² = 26.46

c = 5.1 cm

Area of a Triangle

Example

Find the area of the triangle ABC, a = 8 cm , b = 6 cm <C = 40°.

Area = ½ ab Sin C

= ½ x 8 x 6 x Sin 40° = 15.4 cm²

Questions

1. In triangle ABC, <A = 60°, a = 7 cm, b = 5 cm. Find <B, <C, Side c
2. In triangle ABC, <C = 50°, a = 6 cm, b = 5 cm. Find c.
3. In triangle ABC, a = 18 cm, b = 16 cm, c = 12 cm. Find <C.
4. Find the area of triangle ABC, a = 10.5 cm, b = 8.5 cm and <C = 50°