Question

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

Explanation:

Step1: Recall the triangle - angle - side relationship

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

Step2: Order the side lengths

The side lengths of the triangle are \(12\) (opposite angle \(B\)), \(16\) (opposite angle \(A\)), and \(22\) (opposite angle \(C\)). So, \(12<16 < 22\).

Step3: Order the angles based on the side - angle relationship

Since the side opposite angle \(B\) (\(12\)) is the smallest, angle \(B\) is the smallest. The side opposite angle \(A\) (\(16\)) is the next - smallest, so angle \(A\) is the next - smallest. The side opposite angle \(C\) (\(22\)) is the largest, so angle \(C\) is the largest.

Answer:

angle \(B\), angle \(A\), angle \(C\)