Question

What is the angle between the two straight lines $y=(2-\sqrt{3})x+5$ and $y=(2+\sqrt{3})x-7$?

• A. $60^{\circ }$
• B. $45^{\circ }$
• C. $30^{\circ }$
• D. $15^{\circ }$

Answer 1

Answer: (A)

The given lines are
$y=(2-\sqrt{3})x+5$
and $y=(2+\sqrt{3})x-7$
Therefore, slope of first line $m_1=2-\sqrt{3}$
and slope of second line $m_2=2+\sqrt{3}$
$\therefore \tan \theta =\left|\frac{m_2-m_1}{1+m_1{m}_2}\right|=\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+\left(4-3\right)}\right|$
$=\left|\frac{2\sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi }{3}\Rightarrow \theta =\frac{\pi }{3}=60^{\circ }$