Question

list the sides of each triangle in order from shortest to longest.
△cba with ∠c = 122°, ∠b = 16°, and ∠a = 42°
choose the correct order of the sides from shortest to longest.
○ a. cb, ab, ac
○ b. ac, cb, ab
○ c. ab, ac, cb
○ d. ab, cb, ac
○ e. cb, ac, ab
○ f. ac, ab, cb

Explanation:

Step1: Recall the triangle side - angle relationship

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

Step2: Compare the angles

We have \(\angle B = 16^{\circ}\), \(\angle A=42^{\circ}\), \(\angle C = 122^{\circ}\). So, \(\angle B<\angle A<\angle C\).

Step3: Determine the sides opposite the angles

The side opposite \(\angle B\) is \(AC\), the side opposite \(\angle A\) is \(CB\), and the side opposite \(\angle C\) is \(AB\).

Answer:

F. \(\overline{AC},\overline{AB},\overline{CB}\)