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Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

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Solution:

Given, the line makes an 30° with the positive direction of y-axis measured anticlockwise.

Let the line makes an angle θ with the positive direction of x-axis.

From the above figure, we get

∠OAB = 30°    (Vertically opposite angle)

In ΔAOB,

∠ABO + 30° + 90° = 180°

⇒ ∠ABO = 180° – 120° = 60°

∴ θ = 180°  – ∠ABO = 180° – 60° = 120°

Slope of the line = tan120° = tan (180° – 60°) = –tan60° = -√3

Thus, the slope of the line is -√3.

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