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Asked by BhavSimran | 10 Mar, 2010, 12:05: PM Expert Answer

In ABC, let a, b and c be the lengths of sides opposite to the angles A, B and C respectively.

Draw a perpendicular from vertex A onto side BC. And call it AM.

Let BM = x, so that MC = a-x.

In ABM and ACM we can write using Pythagorus's theorem,

AM2 = c2-x2

AM2 = b2-(a-x)2

So that,

c2 - x2 = b2 - (a - x)2

c2 - x2 = b2 - a2 +2ax -x2

c2 = b2 - a2 +2ax

x = (c2 - b2 + a2)/2a

cosB = x/c

= (c2 - b2 + a2)/2ac

= (a2 + c2 - b2 )/2ac

Similarly we can write the expression for cosA and cosC.

It's called cosine rule.

Regards,

Team,

TopperLearning.

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