In `triangle ABC` , if `angle A = 55^(@), angle B = 75^(@)` then find out the smallest and longest side of the triangle .

Answer

To solve the problem, we need to find the smallest and longest sides of triangle ABC given the angles A and B.

### Step-by-Step Solution:

1. **Identify the Given Angles:**
- We have angle A = 55° and angle B = 75°.

2. **Calculate Angle C:**
- We know that the sum of the angles in a triangle is 180°.
- Therefore, angle C can be calculated as:
\[ \text{Angle C} = 180° - \text{Angle A} - \text{Angle B} \]
- Substituting the known values:
\[ \text{Angle C} = 180° - 55° - 75° = 180° - 130° = 50° \]

3. **List the Angles:**
- Now we have:
- Angle A = 55°
- Angle B = 75°
- Angle C = 50°

4. **Determine the Smallest and Longest Angles:**
- The smallest angle is angle C (50°).
- The longest angle is angle B (75°).

5. **Identify the Sides Opposite to the Angles:**
- The side opposite the smallest angle (Angle C) is side AB.
- The side opposite the longest angle (Angle B) is side AC.

6. **Conclusion:**
- Therefore, the smallest side of triangle ABC is **AB**.
- The longest side of triangle ABC is **AC**.

### Final Answer:
- Smallest side: **AB**
- Longest side: **AC**