A line which is passing through (1,2) 

To Find: The equation of a straight line.

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

Explanation: Here, sin θ = \(\frac{3}{5}\) 

We know, sin θ = \(\frac{perpendicular}{Hypotenues}\) =   \(\frac{3}{5}\)  

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 = \(\frac{Perpendicular}{Base}\) = \(\frac{3}{4}\) 

SO, The slope of the line, m = tan θ

m = \(\frac{3}{4}\) 

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

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

y – 2 = \(\frac{3}{4}\)(x – 1) 

4y – 8 = 3x – 3 

3x – 4y + 5 = 0 

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

Answer:

Equation of the line = 3x - 4y + 5 = 0

Step-by-step explanation:

Given:

• The line passes through the point (1,2)
• It makes an angle with the positive direction of x axis whose sin is 3/5

To Find:

• The equation of the straight line

Solution:

Here we have to first find the slope of the line

We know that,

m = tan θ

where m is the slope.

We know that

sin θ = opposite/hypotenuse = 3/5

Hence by Pythagoras theorem finding the adjacent side,

Adjacent side = √(25 - 9)

Adjacent side = √16 = 4 units

Also,

tan θ = opposite/adjacent = 3/4

Hence slope of the line is 3/4.

Now point slope form of a line is given by,

y - y₀ = m (x - x₀)

Here (1,2) = (x₀, y₀)

Substitute the data,

y - 2 = 3/4 (x - 1)

Multiply whole equation by 4

4y - 8 = 3x - 3

3x - 4y + 5 = 0

Hence the equation of the line is 3x - 4y + 5 = 0