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Given the slope of a line and the angle it makes with another line, how to find the slope of the other line?

SaitamaSensei
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  • Do you know the formula for angle between 2 lines in terms of their slopes ? – Shailesh Oct 30 '16 at 09:30
  • I am aware of that, but isn't it suppose to give two angles for the same pair of lines, I am getting two values for the slope, but I cannot comprehend how is this happening geometrically. – SaitamaSensei Oct 30 '16 at 09:33
  • Take an example. Lets take the X-axis. The lines $y=x$ and $y - -x$ both make an angle of $45$ degrees to the X-axis. ... – Shailesh Oct 30 '16 at 09:45

1 Answers1

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That is pretty easy. Let $\theta_1$ and $m_1$ be the angle and slope if the first line, respectively, $\theta_2$ and $m_2$ be the angle and slope if the second line, respectively, and $\phi$ the angle between $\theta_1$ and $\theta_2$.

Then $\theta_1 = \tan^{-1} m_1$ by the definition of tan.

$$\theta_2=\theta_1+\phi$$.

Since $$m_2=\tan \theta_2$$

Finally, we get:

$$m_2=\tan (\phi +(\tan^{-1} m_1))$$.

teed
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