Question

Fine, and radians in degrees, the inclination theta of the line with the equation -5x - 13y - 66 =0

Answer 1

Given

`-5x-13y-66=0`

Transform it into its slope-intercept form, as shown below

`\begin{gathered} \Rightarrow y=-(5)/(13)x-(66)/(13) \\ \end{gathered}`

Then, the slope of the line is -5/13.

On the other hand, the inclination angle of a line is given by the formula below

`\begin{gathered} m=tan\theta \\ \Rightarrow\theta=\tan^(-1)(m) \\ \theta\rightarrow\text{ inclination angle} \\ m\rightarrow\text{ slope} \end{gathered}`

Therefore, in our case,

`\begin{gathered} \Rightarrow\theta=\tan^(-1)(-(5)/(13)) \\ \Rightarrow\theta=-0.3671738...\text{ radians} \\ or \\ \theta=-21.04\degree \end{gathered}`

Thus, the answer is -0.3671738... radians or -21.04°