Find the slope of the lines whose iclination is given :
`(i) 45^(@)` `(ii) 60^(@)` `(iii) 120^(@)`

Answer

To find the slope of the lines whose inclinations are given, we will use the formula for the slope \( m \) in terms of the angle of inclination \( \theta \):

\[ m = \tan(\theta) \]

Now, let's solve the problem step by step for each given angle of inclination.

### Step 1: For \( \theta = 45^\circ \)

1. **Identify the angle**: The angle of inclination is \( 45^\circ \).
2. **Use the slope formula**: We apply the formula \( m = \tan(45^\circ) \).
3. **Calculate the slope**: We know that \( \tan(45^\circ) = 1 \).
4. **Conclusion**: Therefore, the slope \( m \) for \( 45^\circ \) is \( 1 \).

### Step 2: For \( \theta = 60^\circ \)

1. **Identify the angle**: The angle of inclination is \( 60^\circ \).
2. **Use the slope formula**: We apply the formula \( m = \tan(60^\circ) \).
3. **Calculate the slope**: We know that \( \tan(60^\circ) = \sqrt{3} \).
4. **Conclusion**: Therefore, the slope \( m \) for \( 60^\circ \) is \( \sqrt{3} \).

### Step 3: For \( \theta = 120^\circ \)

1. **Identify the angle**: The angle of inclination is \( 120^\circ \).
2. **Use the slope formula**: We apply the formula \( m = \tan(120^\circ) \).
3. **Use the identity**: We can rewrite \( 120^\circ \) as \( 90^\circ + 30^\circ \). According to the identity \( \tan(90^\circ + \theta) = -\cot(\theta) \), we have:
\[ \tan(120^\circ) = \tan(90^\circ + 30^\circ) = -\cot(30^\circ) \]
4. **Calculate \( \cot(30^\circ) \)**: We know that \( \cot(30^\circ) = \frac{1}{\tan(30^\circ)} = \frac{1}{\frac{1}{\sqrt{3}}} = \sqrt{3} \).
5. **Conclusion**: Therefore, \( \tan(120^\circ) = -\sqrt{3} \), so the slope \( m \) for \( 120^\circ \) is \( -\sqrt{3} \).

### Final Results

- For \( 45^\circ \), the slope is \( 1 \).
- For \( 60^\circ \), the slope is \( \sqrt{3} \).
- For \( 120^\circ \), the slope is \( -\sqrt{3} \).