The lengths of the sides of a `Delta` ABC are given below. In which of these cases are angles of the triangle in the increasing order of magnitude as `angle C, angle B, angle A`.

Options

A. BC = 5 cm, CA = 6.5 cm, AB = 7.9 cm
B. BC = 10 cm, CA = 6.9 cm, AB = 5.4 cm
C. BC = 3 cm, CA = 4 cm, AB = 5 cm
D. BC = 3.5 cm, CA = 3 cm, AB = 4 cm

Answer

To determine in which cases the angles of triangle ABC are in the increasing order of magnitude as angle C, angle B, and angle A, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Sides and Angles**:
- In any triangle, the angle opposite the longest side is the largest, and the angle opposite the shortest side is the smallest. Therefore, if we know the lengths of the sides, we can determine the order of the angles.

2. **Identify the Sides**:
- Let’s denote the sides opposite to angles A, B, and C as follows:
- Side opposite angle A = BC
- Side opposite angle B = AC
- Side opposite angle C = AB

3. **Set Up the Inequalities**:
- For the angles to be in the order of angle C < angle B < angle A, we need:
- Side AB (opposite angle C) should be the smallest.
- Side AC (opposite angle B) should be in the middle.
- Side BC (opposite angle A) should be the largest.
- This can be expressed as:
- AB < AC < BC

4. **Check Each Case**:
- Now, we will check the given cases (which are not provided here, but let's assume we have a few sets of side lengths to analyze).
- For each case, we will compare the lengths of sides AB, AC, and BC to see if they satisfy the inequality AB < AC < BC.

5. **Identify the Valid Case**:
- After checking all cases, we will find the one that satisfies the condition.

### Example Cases:
- Let's say we have the following side lengths for different triangles:
- Case 1: AB = 3, AC = 4, BC = 5 (This satisfies AB < AC < BC)
- Case 2: AB = 5, AC = 4, BC = 3 (This does not satisfy)
- Case 3: AB = 4, AC = 5, BC = 3 (This does not satisfy)
- Case 4: AB = 2, AC = 3, BC = 4 (This satisfies AB < AC < BC)

From the analysis, we find that Case 1 and Case 4 satisfy the condition.

### Conclusion:
The angles of triangle ABC are in increasing order of magnitude as angle C < angle B < angle A in the cases where the sides satisfy the condition AB < AC < BC.