Arrange the angles of the triangle from smallest to largest in the triangle, where the sides are AB = 7 cm, AC = 8 cm, and BC = 9 cm.

Options

A. A,B,C
B. C,B,D
C. C,B,A
D. B,A,C

Answer

To arrange the angles of triangle ABC from smallest to largest based on the given sides, we can follow these steps:

### Step 1: Identify the lengths of the sides
We have the following sides of triangle ABC:
- AB = 7 cm
- AC = 8 cm
- BC = 9 cm

### Step 2: Determine the relationship between sides and angles
In any triangle, the side lengths are directly related to the angles opposite them. Specifically:
- The smallest side is opposite the smallest angle.
- The largest side is opposite the largest angle.

### Step 3: Compare the lengths of the sides
From the given lengths:
- AB (7 cm) is the smallest side.
- AC (8 cm) is the second largest side.
- BC (9 cm) is the largest side.

### Step 4: Identify the angles opposite to each side
Using the property mentioned:
- Angle C is opposite side AB (7 cm).
- Angle B is opposite side AC (8 cm).
- Angle A is opposite side BC (9 cm).

### Step 5: Arrange the angles based on the sides
Since we have established the relationships:
- The smallest angle is opposite the smallest side (Angle C).
- The second largest angle is opposite the second largest side (Angle B).
- The largest angle is opposite the largest side (Angle A).

Thus, we can arrange the angles from smallest to largest:
- Angle C (smallest)
- Angle B (second largest)
- Angle A (largest)

### Final Arrangement
The order of the angles from smallest to largest is:
**Angle C, Angle B, Angle A**