Question

select the correct answer.
which list orders the sides of triangle abc from longest to shortest length?
a.
ac, bc, ab
b.
ab, bc, ac
c.
bc, ac, ab
d.
ac, ab, bc

Explanation:

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

In a triangle, the sum of angles is \(180^{\circ}\). Given \(\angle C = 90^{\circ}\) and \(\angle B=30^{\circ}\), then \(\angle A=180^{\circ}-\angle B - \angle C=180^{\circ}-30^{\circ}-90^{\circ} = 60^{\circ}\)

Step2: Apply the side - angle relationship in a triangle

In a triangle, the larger the angle, the longer the side opposite it.
The sides opposite \(\angle A\), \(\angle B\), and \(\angle C\) are \(BC\), \(AC\), and \(AB\) respectively.
Since \(\angle C(90^{\circ})>\angle A(60^{\circ})>\angle B(30^{\circ})\), the sides opposite them follow the same order. So \(AB>BC > AC\)

Answer:

B. \(AB, BC, AC\)