Question

find the slope of a line which makes an angle of 30 degree with the positive direction of X axis​

Answer 1

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°

Answer 2

Answer:

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.Read more on Sarthaks.com - https://www.sarthaks.com/1845/find-slope-line-which-makes-angle-30-with-positive-direction-axis-measured-anticlockwise