Wang Jimenez
08/07/2023 · Primary School
13) The inclination \( \theta \) of the line with slope \( =\sqrt{3} \) is :
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Step-by-step Solution
The slope \( m \) of a line is related to the angle of inclination \( \theta \) by the formula:
\[
m = \tan(\theta)
\]
Given that the slope \( m = \sqrt{3} \), we can set up the equation:
\[
\tan(\theta) = \sqrt{3}
\]
To find \( \theta \), we need to determine the angle whose tangent is \( \sqrt{3} \). We know that:
\[
\tan(60^\circ) = \sqrt{3}
\]
Thus, the angle of inclination \( \theta \) is:
\[
\theta = 60^\circ
\]
Therefore, the inclination \( \theta \) of the line with slope \( \sqrt{3} \) is:
\[
\theta = 60^\circ
\]
Quick Answer
The inclination \( \theta \) is \( 60^\circ \).
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