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 .


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,


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 (x1,y1) = (1,2)


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


y – 2 = (x – 1)


4y – 8 = 3x – 3


3x – 4y + 5 = 0


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


5
1