Question

For triangle ABC, m(∠A) = 30° and m(∠B)= 115°. Which of the following lists the sides of the triangle from shortest to longest?

1. AC, BC, AB

2. AB, BC, AC

3. AC, AB, BC

4. BC, AB, AC

Answer 1

After finding the measure of the third angle, we determine that the sides of triangle ABC in order from shortest to longest are AC, AB, BC.

Step-by-step explanation:

To determine the order of the sides from shortest to longest in triangle ABC with angles ∠A = 30° and ∠B = 115°, we first deduce ∠C. The sum of angles in a triangle is 180°, so ∠C = 180° - ∠A - ∠B = 180° - 30° - 115° = 35°.

Using the fact that the side opposite the smallest angle in a triangle is the shortest and so on, we find that the side opposite ∠A is the shortest, followed by the side opposite ∠C, and the side opposite ∠B is the longest. Therefore, side AC (opposite the smallest angle) is the shortest, then AB (opposite the next larger angle, ∠C), and BC (opposite ∠B) is the longest.

Hence, the correct order from shortest to longest is AC, AB, BC.