Find the inclination of the line whose slope is ` -1/(sqrt(3))`

Answer

To find the inclination of the line whose slope is \(-\frac{1}{\sqrt{3}}\), we can follow these steps:

### Step 1: Understand the relationship between slope and inclination
The slope \(m\) of a line can be expressed in terms of the angle of inclination \(\theta\) as:
\[ m = \tan(\theta) \]
where \(\theta\) is the angle the line makes with the positive direction of the x-axis.

### Step 2: Set up the equation
Given that the slope \(m = -\frac{1}{\sqrt{3}}\), we can write:
\[ \tan(\theta) = -\frac{1}{\sqrt{3}} \]

### Step 3: Find the angle \(\theta\)
To find the angle \(\theta\), we need to determine the angle whose tangent is \(-\frac{1}{\sqrt{3}}\). We know that:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
Thus, the angle whose tangent is \(-\frac{1}{\sqrt{3}}\) can be found in the second quadrant (since tangent is negative in the second quadrant) and is given by:
\[ \theta = 180^\circ - 30^\circ = 150^\circ \]

### Step 4: Conclusion
Therefore, the inclination of the line is:
\[ \theta = 150^\circ \]

### Final Answer
The inclination of the line whose slope is \(-\frac{1}{\sqrt{3}}\) is \(150^\circ\).

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