Answer:
So, the angle of inclination of the line 2 √ 3x - 6y - 8 = 0 with the OX axis is approximately 60∘ .
Explanation:
To find the angle of inclination (also known as the angle of elevation or slope) of the line 2√3x−6y−8=0 with the positive direction of the x-axis (OX axis), you can use the following formula:
Angle of inclination(θ)=arctan(slope)
First, you need to express the equation of the line in slope-intercept form (y = mx + b), where m is the slope of the line. Let's rearrange the given equation:
2√ 3x − 6y − 8 = 0
2 √ 3x − 6y = 8
2 √ 3x= 6y + 8
Now, divide both sides by 2√ 3 to isolate y:
y = 6 ÷ 2 √ 3x + 8 ÷ 2 √ 3
Simplify:
y = 3 ÷ √ 3x + 4 √ 3 ÷ 3
Now, you can see that the slope (m) of the line is m= 3 ÷ √ 3 To find the angle of inclination, plug this slope into the arctan formula:
θ=arctan( 3 ÷ √ 3)
Now, calculate the angle:
θ=arctan( 3 ÷ √ 3 )≈60∘
So, the angle of inclination of the line 2 √ 3x - 6y - 8 = 0 with the OX axis is approximately 60∘ .