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BodhiAI
Nov. 12, 2019

Sine Rule:

 

 

Sine Rule 

In any

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 ΔABD 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 

Similarly, ...........(1)

From (1) and (2), we have ..........(2)

 


 

Important 

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. 

Let

Then, a = k sin A, b = k sin B, c = k sin C

In any  

Let ABC be any triangle and AD is a perpendicular from A on BC 

and similar other results.