Chapter 6.4, Problem 6CE

To determine

The longest side and the shortest side of the given triangle.

Answer to Problem 6CE

  $GI$ will be greater side and $GH$ will be smaller side.

Explanation of Solution

Given information :

The given triangle is,

The given triangle is $\Delta GHI$ as shown above.

Measure of angles are $\angle G={32}^{°}and\angle H={121}^{°}$

From angle sum property in a triangle

  $\begin{array}{c}\angle G+\angle H+\angle I={180}^{°}\\ {32}^{°}+{121}^{°}+\angle I={180}^{°}\\ \angle I={180}^{°}-\left({32}^{°}+{121}^{°}\right)\\ ={180}^{°}-{153}^{°}\\ ={27}^{°}\end{array}$

From the properties of triangle that sides opposite to greater angle is greater.

Here, the greater angle is $\angle H={121}^{°}$ .

Therefore, the opposite side is $GI$ will be greater.

Similarly,

Sides opposite to smaller angle is smaller.

Here, the smaller angle is $\angle I={27}^{°}$ .

Therefore, the opposite side is $GH$ will be smaller.