Question

Use the law of cosines to write an expression equivalent to b

Answer 1

Given:

A triangle ABC.

The given expression for b is:

$b=\sqrt{m+n-pq}$

To find:

The expression that is equivalent to b.

Solution:

According to the Law of Cosines,

$b^2=a^2+c^2-2ac\cos B$

It can be written as:

$b=\sqrt{a^2+c^2-2ac\cos B}$              ...(i)

We have,

$b=\sqrt{m+n-pq}$                                ...(ii)

On comparing (i) and (ii), we get

$m=a^2$

$n=c^2$

$p=2ac$

$q=\cos B$

Therefore, the required values are $m=a^2,n=c^2,p=2ac,q=\cos B$.