Question

ordering sides list the sides in order from shortest to longest. 14. a c b 60° 80° 40°

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.

Step2: Identify the angles and their opposite sides

• Angle \(A = 60^{\circ}\), side opposite \(A\) is \(BC\).
• Angle \(B=80^{\circ}\), side opposite \(B\) is \(AC\).
• Angle \(C = 40^{\circ}\), side opposite \(C\) is \(AB\).

Step3: Order the angles

Since \(40^{\circ}<60^{\circ}<80^{\circ}\), i.e., \(\angle C<\angle A<\angle B\).

Step4: Order the sides

Using the side - angle relationship, the sides opposite these angles will follow the same order. So, \(AB < BC

Answer:

\(AB < BC