Question

Find the angle of inclination of a line with the given slope. You may use a calculator. $$ \sqrt{3} $$

Short answer

The angle of inclination of the line with a slope of \(\sqrt{3}\) is approximately \(60^\circ\).

Step-by-step solution

Write down the given information

The slope of the line is given as \(\sqrt{3}\).

Use the tangent relationship for the angle of inclination

The tangent of the angle of inclination, denoted as \(\theta\), is equal to the slope of the line: \[\tan(\theta) = \sqrt{3}\]

Find the angle using the arctangent function

To obtain the angle of inclination, we apply the inverse tangent, also known as arctangent, to both sides of the equation: \[\theta = \arctan(\sqrt{3})\]

Use a calculator to evaluate the arctangent expression

Using a calculator, we find the arctangent of \(\sqrt{3}\) in degrees: \[\theta = \arctan(\sqrt{3}) \approx 60^\circ\]

Write the final answer

The angle of inclination of the line with a slope of \(\sqrt{3}\) is approximately \(60^\circ\).