What is the angle between the two straight lines $y=(2-\sqrt{3}) x+5$ and $y=(2+\sqrt{3}) x-7 ?$
- $60^{\circ}$
- $45^{\circ}$
- $30^{\circ}$
- $15^{\circ}$
Solution
$y=(2-\sqrt{3}) x+5 \text { and } y=(2+\sqrt{3}) x-7$
Therefore, slope of first line $=m_1=2-\sqrt{3}$ and slope of second line $=m_2=2+\sqrt{3}$
$\therefore \quad \tan \theta=\left|\frac{m_2-m_1}{1+m_1 m_2}\right|=\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+(4-3)}\right|$
$=\left|\frac{2 \sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{3}=60^{\circ}$
Asked in: BITSAT 2023 (Memory Based Paper 1)