Chapter 6.4, Problem 14WE

To determine

To find: the longest segment.

Answer to Problem 14WE

  $\overline{AB}$ and $\overline{AV}$ are the longest sides.

Explanation of Solution

Given Information:

Given diagram,

  

Calculation:

Consider the theorem,

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

First draw the diagram to scale as below:

  

From the above figure it can be calculated that $\angle VAC$ and $\angle BAC$ .

As sides $VA$ and $AC$ are equal hence $\angle VAC$ and $\angle AVC$ is equal.

Let $\angle AVC=x$ then,

  $\begin{array}{c}x+x+70°=180°\\ x=55°\end{array}$

Hence, $\angle CAV=55°$

Similarly, $\angle CAB=55°$

Therefore, according to the above theorem, $AB$ and $AV$ will be the longest sides.

Therefore, $\overline{AB}$ and $\overline{AV}$ are the longest sides.