Question

Angle made by a line with the positive direction of X-axis is 30\(^\circ\). Find slope of that line.

Hint:

Memorize the standard tangent values for common angles: \(\tan(0^\circ)=0\), \(\tan(30^\circ)=\frac{1}{\sqrt{3}}\), \(\tan(45^\circ)=1\), \(\tan(60^\circ)=\sqrt{3}\). For \(\tan(90^\circ)\), the slope is undefined (vertical line).

Answer 1

Step 1: Understanding the Concept:
The slope (or gradient) of a line is a number that describes both the direction and the steepness of the line. The slope 'm' is related to the angle of inclination '\(\theta\)' (the angle the line makes with the positive direction of the x-axis) by the tangent function.

Step 2: Key Formula or Approach:
The slope \(m\) of a line is given by: \[ m = \tan(\theta) \] where \(\theta\) is the angle of inclination.

Step 3: Detailed Explanation:
Given: \[\begin{array}{rl} \bullet & \text{The angle of inclination, \(\theta = 30^\circ\).} \\ \end{array}\] Using the formula for the slope: \[ m = \tan(30^\circ) \] We know the standard trigonometric value: \[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \] Therefore, the slope of the line is \( \frac{1}{\sqrt{3}} \).

Step 4: Final Answer:
The slope of the line is \( \frac{1}{\sqrt{3}} \).