Chapter 6.4, Problem 4CE

To determine

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

Answer to Problem 4CE

  $BC$ will be greater side and $AC$ will be smaller side.

Explanation of Solution

Given information :

The given triangle is,

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

Measure of angles are $\angle A={75}^{°}and\angle C={70}^{°}$

From angle sum property in a triangle

  $\begin{array}{c}\angle A+\angle B+\angle C={180}^{°}\\ {75}^{°}+\angle B+{70}^{°}={180}^{°}\\ \angle B={180}^{°}-\left({75}^{°}+{70}^{°}\right)\\ ={180}^{°}-{145}^{°}\\ ={35}^{°}\end{array}$

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

Here, the greater angle is $\angle A={75}^{°}$ .

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

Similarly,

Sides opposite to smaller angle is smaller.

Here, the smaller angle is $\angle B={35}^{°}$ .

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