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

Question: Line l pass through two points P_{1}(1, 0) and p_{2}(0, Sqrt (3)), find the angle a.

Solution:

Because the point P_{1} has the coordinate (1, 0), so, x_{1} = 1 and y_{1} = 0

Because the point P_{2} has the coordinate (0, Sqrt (3)), so, x_{2} = 0 and y_{2} = Sqrt (3)

The slope (k) of the line is, k = (y_{2} - y_{1})/x_{2} = x_{1}) = [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 60^{o} = Sqrt (3), so, arc(tan(Sqrt (3))) = 60^{o}

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

Therefore, the angle a is 120^{o}

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