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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

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