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 the triangle angle - side relationship

In a triangle, the larger the length of a side, the larger the measure of the angle opposite that side. So we first identify the sides opposite each angle.

• Side opposite angle \(A\): \(BC = 16\)
• Side opposite angle \(B\): \(AC = 12\)
• Side opposite angle \(C\): \(AB = 22\)

Step2: Order the sides from smallest to largest

The lengths of the sides are \(12\) ( \(AC\) ), \(16\) ( \(BC\) ), and \(22\) ( \(AB\) ). So in order from smallest to largest: \(AC

Step3: Order the angles based on opposite sides

Since the side opposite angle \(B\) is \(AC = 12\) (smallest side), angle \(B\) is the smallest angle. The side opposite angle \(A\) is \(BC = 16\), so angle \(A\) is the next. The side opposite angle \(C\) is \(AB = 22\) (largest side), so angle \(C\) is the largest angle. So the order of angles from smallest to largest is angle \(B\), angle \(A\), angle \(C\)

Answer:

B. angle B, angle A, angle C