Question

Find the inclination of a line whose slope is: $\sqrt 3$.

Answer 1

Here in this problem, we need to find the inclination of a given line. The line’s slope is given to be $\sqrt 3$. Equaling this with $\tan \theta$ we will get our desired angle.

Complete step by step solution:
We are given,
Slope of line $= \sqrt 3$,
We know,
Slope of line $= {\text{ tan}}\theta$
Then, we also get, $\sqrt 3 = {\text{tan}}\theta$
Since $tan{\text{ }}60^\circ {\text{ }} = {\text{ }}\sqrt 3$
We get, $\theta = {\text{ }}60^\circ {\text{ }}$

Hence, the angle of inclination of the line is $60^\circ$.

Note:
If a straight line makes an angle $\theta$ with the positive x-axis. This is called the angle of inclination of a straight line.

1. For Vertical lines
   $\theta = 90^\circ$
   The gradient is undefined since there is no change in the x-values.
2. For Horizontal lines
   $\theta = 0^\circ$
   The gradient is equal to 0 since there is no change in the y-values