Finding Angle of Inclination of a Line

That's the angle that the line makes with the horizontal. Okay? So if you were to draw on horizontal line, that angle that it makes with that line. And you can see here that the formula is equals the tangent of theta. So is the slope. Okay? The slope of the line is equal to the tangent of the angle of the line that it makes with the horizontal. So if you look at this diagram here, you can see that here's your angle theta. And the tangent of theta equals opposite over adjacent. Right? Remember your tangent ratio opposite over adjacent. SOAOA, right? So tangent of theta is opposite or adjacent, which is the change in over the change in which equals the slope. Now, if you want to solve for the angle, all you have to do is take the tangent inverse of both sides of this equation. Okay? So the tangent inverse and you can see you're going to get theta by itself. So theta is the tangent inverse of the slope. So let's take look at some examples and you'll you'll see how this works. So in this first example, we've got 3x + 2 = 6. First thing we want to do is we want to find the slope of the line. So the way we do that is we rearrange it into the slope intercept form, which is the y= mx plus form. So we're going to get by itself. Divide everything by 2, we get = -3x + 3. So what we're interested in is this value here, the number in front of the That's the slope, right? = mx + So we know the slope is -3. So we have -3 equals the tangent of the but by taking the tangent inverse of both sides we get theta equ= tangent inverse of -3. Now let's go ahead and go to the calculator take look at what that value is. So we've got tangent inverse of -36.3. Okay. Now if we look at 56.3 let's graph this line real quick so we can see what this looks like. So we have intercept of 6. So that's somewhere, let's see, 1 2 3 4 5 6. Right about there. Has slope of -3. So that's down 3 over 1. So it looks something like this. If we draw horizontal line, okay, the angle at 56° that we're getting is that angle right there. Now, when you find the angle of inclination, you really want it to be positive angle between 0° and 180° like that. Okay? So the way you do that if you get negative angle is just go ahead and add 180°. That's going to give you this positive angle that it makes with the horizontal. So we're going to do that right now. Let's just add 180°.