Question

How to Find Angle between Lines
Derive the Equation..!​

Answer 1

$\huge\star{\sf{\underline{\blue{DeriVation:}}}}\star$

Let lines be y= m$_{1}$x$_{1}$ + c$_{1}$ and y=m$_{2}$x$_{2}$ + c$_{2}$ and angle between both line is $\bold\theta$

$\theta + \theta_{1} = \theta_{2}$

$\implies$ Tan$\theta$ = Tan($\theta_{2} - \theta_{1}$

$\implies$Tan$\theta$ =$\dfrac{Tan\theta_{2} - Tan\theta_{1}}{1+ Tan\theta_{1}Tan\theta_{2}}$

We know that Tan$\theta$=slope = m

Therefore,

Tan$\theta$=$\left|\frac{m_2 - m_1}{1+m_1m_2}\right|$

$\theta$=Tan$^{-1}\left|\frac{ m_2-m_1}{1+m_1m_2}\right|$