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# Find the angle between the lines whose slopes are

Question:

Find the angle between the lines whose slopes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$.

Solution:

To find out the angle between two lines, the angle is equal to the difference in θ.

The slope of a line $=\tan \theta=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$

So slope of the first line $=\sqrt{3}=\tan \theta_{1} \Rightarrow \tan \theta_{1}=\sqrt{3}$

$\Rightarrow \theta_{1}=\tan ^{-1}(\sqrt{3})$

$\Rightarrow \theta_{1}=60^{\circ}$

The slope of the second line $=\frac{1}{\sqrt{3}}=\tan \theta_{2} \Rightarrow \theta_{2}=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\Rightarrow \theta_{2}=30^{\circ}$

Now the difference between the two lines is $\theta_{1}-\theta_{2}$

$=60^{\circ}-30^{\circ}$

$=30^{\circ}$