Question

Find the angle between the pair of straight lines:
$y=(2-\sqrt{3})x+5$ and $y=(2+\sqrt{3})x-7$

Answer 1

Given lines are $y=(2-\sqrt{3})x+5$ and $y=(2+\sqrt{3})x-7$

$\tan \theta =\left|\frac{m_2-m_1}{1+m_{2}m1}\right|$

From given straight lines $m_1=2-\sqrt{3}$ and $m_2=2+\sqrt{3}$

Substitute above values in $\tan \theta$, we get

$\tan \theta =\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+(4-3)}\right|$

$\Rightarrow tan\theta =\left|\frac{2\sqrt{3}}{2}\right|$

$\Rightarrow \theta ={\tan }^{-1}\sqrt{3}$

Therefore angle is $\theta ={60}^0$