Chapter 6.4, Problem 8WE

To determine

To find: the largest angle

Answer to Problem 8WE

Angle numbered $1$ is the largest angle.

Explanation of Solution

Formula used:

Angle opposite to the larger side is greater than the angle opposite to the shorter side.

Calculation:

  

In $\Delta ABC$ ,

  $\begin{array}{l}AB=x+1\\ BC=x\\ AC=x-1\end{array}$

As dimension is always positive, $x>0$

For $x>0$ ,

  $x-1<x<x+1$

So,

  $AC<BC<AB$

That is $AB$ is the longest side.

Angle opposite to $AB$ is $\angle C$ which is numbered as $1$ .

So,

Angle numbered $1$ is the largest angle.