BodhiAI

Nov. 12, 2019

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 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**

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**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 **

** **

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

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** and similar other results.**