Chapter 15, Problem 1RP

To determine

To Arrange: The angles in the order of smallest to largest.

Answer to Problem 1RP

  $\angle A<\angle B<\angle C$

Explanation of Solution

Given:

  

  $\begin{array}{l}\text{in }\Delta \text{ABC,}\\ AB>AC>BC\end{array}$

Formula Used:

Base-Angle Theorem: It states that in a triangle angle opposite to larger side is always larger and smallest side is smallest and vice-versa.

Calculation:

  $\begin{array}{l}\text{Since AB is the largest side}\\ \angle \text{C is the largest angle}\text{.}\\ \text{As BC}\text{}\text{ is the smallest side }\\ \angle \text{A is the smallest angle}\\ \text{⇒}\angle A<\angle B<\angle C\end{array}$

Conclusion:

Thus the arrangement is $\angle A<\angle B<\angle C$