Question

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

• A. $30^{\circ }$
• B. $60^{\circ }$
• C. $45^{\circ }$
• D. $95^{\circ }$

Answer 1

Answer: (B)

Given equation of straight lines are
$y=(2-\sqrt{3})x+5$
and $y=(2+\sqrt{3})x-7$
On comparing with $y=mx+c$, we get
$m_1=2-\sqrt{3}$
and $m_2=2+\sqrt{3}$
$\therefore \tan \theta =\frac{m_2-m_1}{1+m_1{m}_2}$
$=\frac{2+\sqrt{3}-(2-\sqrt{3})}{1+(2-\sqrt{3})(2+\sqrt{3})}$
$=\frac{2\sqrt{3}}{1+(4-3)}=\frac{2\sqrt{3}}{1+4-3}$
$\Rightarrow \tan \theta =\frac{2\sqrt{3}}{2}=\sqrt{3}$
$\Rightarrow \theta =60^{\circ }$