Question

82° 58° b c ∠c ∠b ac ∠a bc shortest side → ab longest side → smallest angle → largest angle →

Explanation:

Step1: Find the measure of ∠C

The sum of angles in a triangle is \(180^{\circ}\).
\(\angle A = 82^{\circ}\), \(\angle B=58^{\circ}\)
\(\angle C=180^{\circ}-\angle A - \angle B\)
\(\angle C=180^{\circ}-82^{\circ}-58^{\circ}=40^{\circ}\)

Step2: Relate angles and sides

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

• For the longest side:

The largest angle is \(\angle A = 82^{\circ}\), and the side opposite \(\angle A\) is \(BC\).

• For the smallest angle:

\(\angle C = 40^{\circ}\) is the smallest angle.

• For the largest angle:

\(\angle A = 82^{\circ}\) is the largest angle.

Answer:

longest side \(
ightarrow BC\)
smallest angle \(
ightarrow\angle C\)
largest angle \(
ightarrow\angle A\)