Question

list the angles of triangle abc from the smallest to the largest
ab = 17, bc = 21, ac = 18
b,c,a
c,b,a
a,b,c
b,a,c

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the side length, the larger the angle opposite to it. So we first identify the sides and their opposite angles. In triangle \(ABC\), side \(AB\) is opposite angle \(C\), side \(BC\) is opposite angle \(A\), and side \(AC\) is opposite angle \(B\).

Step2: Order the side lengths

We are given \(AB = 17\), \(BC=21\), \(AC = 18\). Ordering these side lengths from smallest to largest: \(AB=17

Step3: Order the angles based on opposite sides

Since \(AB\) (opposite \(\angle C\)) is the shortest, \(\angle C\) is the smallest. Then \(AC\) (opposite \(\angle B\)) is the next, so \(\angle B\) is the next. Then \(BC\) (opposite \(\angle A\)) is the longest, so \(\angle A\) is the largest. So the order of angles from smallest to largest is \(\angle C\), \(\angle B\), \(\angle A\) (i.e., \(C,B,A\)).

Answer:

C,B,A (corresponding to the option with the diamond symbol: C,B,A)