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Find the angle of inclination of the line 2√3 x - 6y - 8 = 0 with the OX axis

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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∘ .

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