Use the law of cosines to write an expression equivalent to b
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Given:
A triangle ABC.
The given expression for b is:
[tex]b=\sqrt{m+n-pq}[/tex]
To find:
The expression that is equivalent to b.
Solution:
According to the Law of Cosines,
[tex]b^2=a^2+c^2-2ac\cos B[/tex]
It can be written as:
[tex]b=\sqrt{a^2+c^2-2ac\cos B}[/tex] ...(i)
We have,
[tex]b=\sqrt{m+n-pq}[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=a^2[/tex]
[tex]n=c^2[/tex]
[tex]p=2ac[/tex]
[tex]q=\cos B[/tex]
Therefore, the required values are [tex]m=a^2,n=c^2,p=2ac,q=\cos B[/tex].