Q. 54.8( 4 Votes )

# Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x – axis whose sine is .

Answer :

A line which is passing through (1,2)

To Find: The equation of a straight line.

Formula used: The equation of line is [y – y_{1} = m(x – x_{1})]

Explanation: Here,

We know,

According to Pythagoras theorem,

(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}

(5)^{2} = (Base)^{2} + (3)^{2}

(Base) =

(Base)^{2} =

Base = 4

Hence,

SO, The slope of the line, m = tan θ

m =

The line passing through (x_{1},y_{1}) = (1,2)

The required equation of line is y – y_{1} = m(x – x_{1})

y – 2 = (x – 1)

4y – 8 = 3x – 3

3x – 4y + 5 = 0

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

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