Question

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

Answer 1

Hint:
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