sine and cosine Rules
Contents
Contents
- Sine Rule
- Cosine Rule
- Area of a Triangle
Sine Rule
Sine Rule
Example
In triangle ABC, <A = 50° , a = 8 cm , b = 6 cm. Find <B, <C, Side c
Cosine Rule
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
Example
In triangle ABC, a = 8 cm , b = 6 cm , c = 9 cm. Find <C.
Area of a Triangle
Area of a Triangle
Area of a triangle (given two sides and angle in-between the two sides) is
½ ab Sin C
(or) ½ bc Sin A
(or) ½ ca Sin B.
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
Questions
- In triangle ABC, <A = 60°, a = 7 cm, b = 5 cm. Find <B, <C, Side c
- In triangle ABC, <C = 50°, a = 6 cm, b = 5 cm. Find c.
- In triangle ABC, a = 18 cm, b = 16 cm, c = 12 cm. Find <C.
- Find the area of triangle ABC, a = 10.5 cm, b = 8.5 cm and <C = 50°