Question

in $delta abc$, $bc = 9$, $ca = 17$, and $ab = 13$. which list has the angles of $delta abc$ in order from largest to smallest?
answer
$mangle b$, $mangle a$, $mangle c$
$mangle c$, $mangle a$, $mangle b$
$mangle c$, $mangle b$, $mangle a$
$mangle a$, $mangle b$, $mangle c$
$mangle b$, $mangle c$, $mangle a$
$mangle a$, $mangle c$, $mangle b$

Explanation:

Step1: Recall angle - side relationship

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

Step2: Identify side lengths

Given \(BC = 9\), \(CA=17\), \(AB = 13\). The longest side is \(CA = 17\), the middle - length side is \(AB = 13\), and the shortest side is \(BC = 9\).

Step3: Determine opposite angles

The angle opposite \(CA\) is \(\angle B\), the angle opposite \(AB\) is \(\angle C\), and the angle opposite \(BC\) is \(\angle A\). So the order of angles from largest to smallest is \(\angle B\), \(\angle C\), \(\angle A\).

Answer:

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