Sine and Cosine Rule

Sine and Cosine Rule

The Sine Rule

The sine rule is an important rule for relating the sides and angles of any given triangle, it doesn't have to be right-angled! (Thats the awesomeness of this rule), It can be any triangle:

Let  a, b and c are the lengths of the sides opposite to the angles of the Triangle A, B and C, as given in the figure, then:

a	=	b	=	c
sinA		sinB		sinC

If we wanted to find an angle, we can re-write this as:

sinA	=	sinB	=	sinC
a		b		c

(The above equation is the only rearrangement of the sine rule)

The Cosine Rule

This is also applicable to any triangle given to relate betweensides and angles:

Let a, b and c are the lengths of the sides opposite to the angles of the Triangle A, B and C, then:

c² = a² + b² - 2abcosC

which can also be written as:

a² = b²+ c² - 2bccosA

The area of a triangle

The area of any triangle is ½absinC (using the above notation).

The formulae for Area of the triangle is ½X(multiple of two sides)X(sine of 3rd angle) as one is given above.

This formula is useful if you don't know the height of a triangle (since you need to know the height for ½ base × height).