Given:

A line which is passing through (2, 2√3), the angle is 75°.

By using the formula,

The equation of line is [y – y₁ = m(x – x₁)]

Here, angle, θ = 75°

The slope of the line, m = tan θ

m = tan 75°

= 3.73 = 2 + √3

The line passing through (x₁, y₁) = (2, 2√3)

The required equation of the line is y – y₁ = m(x – x₁)

Now, substitute the values, we get

y – 2√3 = 2 + √3 (x – 2)

y – 2√3 = (2 + √3)x – 7.46

(2 + √3)x – y – 4 = 0

∴ The equation of the line is (2 + √3)x – y – 4 = 0

A line which is passing through (2,2√3), the angle is 75°. 

To Find: The equation of a straight line. 

Formula used: The equation of line is [y – y₁ = m(x – x₁)] 

Explanation: Here, angle, θ = 75° 

So, The slope of the line, m = tan θ 

m = tan 75°

m = 3.73 = 2 + √3  

The line passing through (x₁,y₁) = (2,2√3) 

The required equation of the line is y – y₁ = m(x – x₁) 

y – 2√3 = 2 + √3 (x – 2) 

y – 2√3 = (2 + √3)x – 7.46 

(2 + √3)x – y – 4 = 0 

Hence, The equation of the line is (2 + √3)x – y – 4 = 0