Question

Question was provided via image upload.

Explanation:

Step1: Find angle at B

In a triangle, the sum of angles is \(180^\circ\). So, \(\angle B = 180^\circ - 40^\circ - 60^\circ = 80^\circ\).

Step2: Relate angles to sides

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

• Opposite \(\angle A = 40^\circ\) is \(BC\) (side \(a\)).
• Opposite \(\angle C = 60^\circ\) is \(AB\) (side \(c\)).
• Opposite \(\angle B = 80^\circ\) is \(AC\) (side \(b\)).

Since \(40^\circ < 60^\circ < 80^\circ\), the order of sides from shortest to largest is \(BC\), \(AB\), \(AC\).

Answer:

\(\overline{BC}\), \(\overline{AB}\), \(\overline{AC}\) (or in terms of options: c. \(\overline{BC}\), b. \(\overline{AB}\), a. \(\overline{AC}\))