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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 45o, that angle B is 30o and that the length b is 2 units.
We know that angle A in the triangle above is 45o, that angle B is 30o 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 180o.
Since we know A and B add up to 75o, the angle C must be 105o.
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(105o)/sin(30o) which is 4sin(105o).
We can write sin(105o) as sin(150o-45o) then use the sin(A-B) rule to write this as sin(150o)cos(45o)-cos(150o)sin(45o)
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
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