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=√(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=√(a^2+c^2-2ac\cos B)` ...(i)

We have,

`b=√(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`.