Question

list the sides of each triangle in order from shortest to longest.
δcba with ∠c = 122°, ∠b = 16°, and ∠a = 42°
choose the correct order of the sides from shortest to longest.
a. overline{cb}, overline{ab}, overline{ac}
b. overline{ac}, overline{cb}, overline{ab}
c. overline{ab}, overline{ac}, overline{cb}
d. overline{ab}, overline{cb}, overline{ac}
e. overline{cb}, overline{ac}, overline{ab}
f. overline{ac}, overline{ab}, overline{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 \(\overline{AC}\), the side opposite \(\angle A\) is \(\overline{CB}\), and the side opposite \(\angle C\) is \(\overline{AB}\).

Answer:

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