Question

The angle measures of $\triangle ABC$ are $A=30\degree$ , $B=40\degree$ , and $C=110\degree$ . List the sides of the triangle in order from shortest to longest.

Answer 1

To list the sides of triangle ABC from shortest to longest, use the rule that the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle: BC is the shortest, AC is middle-length, and AB is the longest.

Step-by-step explanation:

In triangle ABC with angles A=30°, B=40°, and C=110°, we can determine the lengths of the sides based on the angles. In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Therefore, the side opposite angle C, which is side AB, is the longest, and the side opposite angle A, which is side BC, is the shortest. Following this logic, the side opposite angle B, which is side AC, is the middle-length side.

Listing the sides from shortest to longest, we have:

1. BC (opposite the 30° angle)
2. AC (opposite the 40° angle)
3. AB (opposite the 110° angle)