Question

list the sides of the triangle in order from shortest to longest. note that the figure is not drawn to scale. choose the correct order of the sides from shortest to longest. a. \\( \overline { c a }, \overline { b a }, \overline { c b } \\) b. \\( \overline { c b }, \overline { c a }, \overline { b a } \\) c. \\( \overline { b a }, \overline { c b }, \overline { c a } \\) d. \\( \overline { b a }, \overline { c a }, \overline { c b } \\) e. \\( \overline { c b }, \overline { b a }, \overline { c a } \\) f. \\( \overline { c a }, \overline { c b }, \overline { b a } \\)

Explanation:

Step1: Find the measure of angle \( B \)

The sum of angles in a triangle is \( 180^{\circ} \). Let \( \angle B=x \). Then \( x + 78^{\circ}+12^{\circ}=180^{\circ} \). So \( x=180^{\circ}-(78^{\circ} + 12^{\circ})=90^{\circ} \).

Step2: Recall the side - angle relationship in a triangle

In a triangle, the side opposite the smaller angle is shorter. The side opposite \( \angle A = 12^{\circ} \) is \( CB \), the side opposite \( \angle C=78^{\circ} \) is \( BA \), and the side opposite \( \angle B = 90^{\circ} \) is \( CA \). Since \( 12^{\circ}<78^{\circ}<90^{\circ} \), then \( CB

Answer:

C. \( \overline{BA},\overline{CB},\overline{CA} \)