Find the equation of the straight line which passes through the point (1, 2) and makes such an angle with the

A line which is passing through (1, 2)

To Find: The equation of a straight line.

By using the formula,

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

Here, sin θ = \( \dfrac{ 3}{5} \)

We know, sin θ = \( \dfrac{ 3}{5} \)

So, according to Pythagoras theorem,

(Hypotenuse)² = (Base)² + (Perpendicular)²

(5)² = (Base)² + (3)²

(Base) = \( \sqrt{(25 – 9)}\)

(Base)² = \( \sqrt{16}\)

Base = 4

Hence, tan θ = \( \dfrac{ 3}{4} \)

The slope of the line, m = tan θ

=\( \dfrac{ 3}{4} \)

The line passing through (x₁,y₁) = (1,2)

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

Now, substitute the values, we get

y – 2 = (\( \dfrac{ 3}{4} \)) (x – 1)

4y – 8 = 3x – 3

3x – 4y + 5 = 0

The equation of line is 3x – 4y + 5 = 0