Chapter 6.4, Problem 5CE

To determine

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

Answer to Problem 5CE

  $FD$ will be greater side and $ED$ will be smaller side.

Explanation of Solution

Given information :

The given triangle is

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

Measure of angles are $\angle F={43}^{°}and\angle E={90}^{°}$

From angle sum property in a triangle

  $\begin{array}{c}\angle E+\angle F+\angle D={180}^{°}\\ {90}^{°}+{43}^{°}+\angle D={180}^{°}\\ \angle D={180}^{°}-\left({90}^{°}+{43}^{°}\right)\\ ={180}^{°}-{133}^{°}\\ ={47}^{°}\end{array}$

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

Here, the greater angle is $\angle E={90}^{°}$ .

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

Similarly,

Sides opposite to smaller angle is smaller.

Here, the smaller angle is $\angle F={43}^{°}$ .

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