what is sine rule?

Hi,

The Sile rule or the law of sines states that, for any triangle ABC,

sin(A)/a = sin(B)/b = sin(C)/c,

where A,B and C are the angles of the triangles and a,b,c are the lengths of the sides opposite to each of these angles.

This allows us to work out any length and angle that we don't know, provided we do know some of the lengths and angles in the triangle.

An example :

Suppose we know that angle A in the triangle above is 45^o, that angle B is 30^o and that the length b is 2 units.

We know that angle A in the triangle above is 45^o, that angle B is 30^o and that the length b is 2 units.

To work out the remaining angle, we need to remember that the angles within a triangle always add up to 180^o.

Since we know A and B add up to 75^o, the angle C must be 105^o.

Now to find the length a, we can use the first part of the sine rule above. We can rearrange a/sinA = b/sinB to get a=bsinA/sinB.

Since we know A and B we can evaluate this expression to get
a=

Finally we can use the second part of the sine rule to find the length c:

b/sinB=c/sinC, so c=bsinC/sinB

That gives c=2sin(105^o)/sin(30^o)
which is 4sin(105^o).

We can write sin(105^o) as sin(150^o-45^o) then use the sin(A-B) rule to write this as
sin(150^o)cos(45^o)-cos(150^o)sin(45^o)

Putting in the values for the sine and cosine of these special angles gives
c=

Hi

Sine Rule

Case 1 (If A is an acute angle)

Consider angle A

Now      ÐBAC = ÐBPC (Ðs in same segment)

Now  ÐBAC + ÐBPC = 180° (opp.  of cyclic quad.) 

SinA/a = SinB/b = SinC/c

this is sine  rule where A B C are angles of triangles and a b c are are opposite sides

its used for relating sides and angles of a triangle

it states that side a/sin A =side b/sin B =side c/sin c