Find the angle between the positive x-axis and the line

Question: Line l pass through two points P₁(1, 0) and p₂(0, square root of 3), find the angle a.

Solution:

Because the point P₁ has the coordinate (1, 0), so, x₁ = 1 and y₁ = 0

Because the point P₂ has the coordinate (0, square root of 3), so, x₂ = 0 and y₂ = square root of 3

The slope (k) of the line is, k = (y₂ - y₁)/x₂ = x₁) = (square root of 3 - 0)/(0 - 1) = (square root of 3)/(-1) = -(square root of 3)

The slope k is tan(a), so, tan(a) = -(square root of 3)

Because tan(a) is negative, so the angle a is in quadrant II, so the angle a = pi - arc(tan(square root of 3))

Note: In a right triangle, tan 60^o = square root of 3, so, arc(tan(square root of 3)) = 60^o

so, the angle a = 180^o - 60^o = 120^o

Therefore, the angle a is 120^o