The three angles of a triangle are in the ratio `3:4:5`. Then the angles respectively are:

Options

A. `45^(@), 60^(@), 75^(@)`
B. `60^(@), 45^(@), 75^(@)`
C. `60^(@), 75^(@), 45^(@)`
D. `75^(@), 60^(@), 45^(@)`

Answer

To solve the problem of finding the angles of a triangle given their ratio of 3:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the triangle are given in the ratio of 3:4:5. This means we can express the angles in terms of a variable. Let the angles be represented as:
- Angle A = 3x
- Angle B = 4x
- Angle C = 5x

2. **Use the Angle Sum Property**: The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
\[ 3x + 4x + 5x = 180 \]

3. **Combine Like Terms**: Add the coefficients of x:
\[ 12x = 180 \]

4. **Solve for x**: To find the value of x, divide both sides of the equation by 12:
\[ x = \frac{180}{12} = 15 \]

5. **Calculate Each Angle**:
- Angle A = 3x = 3 * 15 = 45 degrees
- Angle B = 4x = 4 * 15 = 60 degrees
- Angle C = 5x = 5 * 15 = 75 degrees

6. **Final Angles**: Thus, the angles of the triangle are:
- Angle A = 45 degrees
- Angle B = 60 degrees
- Angle C = 75 degrees

### Summary of the Angles:
The angles of the triangle are 45 degrees, 60 degrees, and 75 degrees.