Question

From the adjoining figure, find:

1. The longest side of ABC
2. The smallest side of ΔABC.

Answer 1

Given:

• Exterior angles shown: at A = 110°, at B on the line through B = 128°, at C on the line through C = 122°.
• Reminder: in a triangle the larger interior angle is opposite the longer side and the smaller interior angle is opposite the shorter side.

Step-wise calculation:

1. Find interior angles from the exterior angles:

∠A = 180° – 110° = 70°

∠B = 180° – 128° = 52°

∠C = 180° – 122° = 58°   ...(Check: 70° + 52° + 58° = 180°)

2. Compare the interior angles:

Largest angle = ∠A = 70°

Smallest angle = ∠B = 52°

3. Use the opposite-side rule:

The longest side is opposite the largest angle ∠A → side BC.

The smallest side is opposite the smallest angle ∠B → side AC.