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Q.
What is the angle between the two straight lines
$y=(2-\sqrt{3}) x+5$ and $y=(2+\sqrt{3}) x-7 ?$
Straight Lines
Solution:
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+(4-3)}\right|$
$=\left|\frac{2 \sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi}{3}$
$ \Rightarrow \theta=\frac{\pi}{3}=60^{\circ} $