i.e. the sines of the angles are proportional to the lengths of the opposite sides.
Let A, B and C are the vertices of a ΔABC and AD be perpendicular from A on BC.
In we have
sin B =AD/AB
AD = csin B
Also, in ΔADCwe have
sin C =AD/AC
AD = b sinC
AD = b sin C = c sin B
From (1) and (2), we have ..........(2)
The above rule can also be written as
The sine rule is generally used to express sides of the triangle in terms of sines of angles and vice-versa.
Then, a = k sin A, b = k sin B, c = k sin C
Let ABC be any triangle and AD is a perpendicular from A on BC
and similar other results.