Find the angle between the positive x-axis and the line
Question: Line l pass through two points P1(1, 0) and p2(0, Sqrt (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, Sqrt (3)), so, x2 = 0 and y2 = Sqrt (3)
The slope (k) of the line is, k = (y2 - y1)/x2 = x1) = [Sqrt (3) - 0]/(0 - 1) = (Sqrt (3))/(-1) = -Sqrt (3)
The slope k is tan(a), so, tan(a) = -Sqrt (3)
Because tan(a) is negative, so the angle a is in quadrant II, so the angle a = pi - arc(tan(Sqrt (3)))
Note: In a right triangle, tan 60o = Sqrt (3), so, arc(tan(Sqrt (3))) = 60o
so, the angle a = 180o - 60o = 120o
Therefore, the angle a is 120o