Find the angle which the line joining the points

Question:

Find the angle which the line joining the points

$(1, \sqrt{3})$ and $(\sqrt{2}, \sqrt{6})$ makes with the $x$-axis.

 

Solution:

To find angle, we will find slope using two points

$\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{(\sqrt{6})-(\sqrt{3})}{(\sqrt{2})-1}=\frac{(\sqrt{3})((\sqrt{2})-1)}{((\sqrt{2})-1)}$

$\mathrm{m}=\sqrt{3}$

Now as we have m = tanθ

$\tan \theta=(\sqrt{3}) \Rightarrow \theta=60^{\circ}$

So, angle line makes with the positive $x$-axis is $60^{\circ}$.

 

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