Question

consider the triangle. which shows the order of the angles from smallest to largest? angle a, angle b, angle c angle b, angle a, angle c angle b, angle c, angle a angle c, angle a, angle b

Explanation:

Step1: Recall angle - side relationship

In a triangle, the smallest angle is opposite the shortest side and the largest angle is opposite the longest side.

Step2: Identify side lengths

The side lengths of the triangle are \(AC = 12\), \(BC=16\), and \(AB = 22\).

Step3: Match angles to sides

The angle opposite \(AC\) is \(\angle B\), the angle opposite \(BC\) is \(\angle A\), and the angle opposite \(AB\) is \(\angle C\).
Since \(12<16<22\), the order of the angles from smallest to largest is \(\angle B,\angle A,\angle C\).

Answer:

angle B, angle A, angle C