SOLUTION: please help me solve this question "if the length of perpendicular from the origin to a line is 5 units and its angle is 120 degrees then what is the equation of line?

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Question 465958: please help me solve this question "if the length of perpendicular from the origin to a line is 5 units and its angle is 120 degrees then what is the equation of line?
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
please help me solve this question "if the length of perpendicular from the origin to a line is 5 units and its angle is 120 degrees then what is the equation of line?
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Using trigonometry terminology, rotating the perpendicular 120� places the point of intersection of the perpendicular and line in quadrant II. You are now working with a reference angle of 60�. The slope of the perpendicular=tan 60�=-√3 in quadrant II. You also have a right triangle to work with where the hypotenuse=length of the perpendicular=5, and legs=(x,y) coordinates of the intersection.
x=5 cos 60�=5*-1/2=-5/2=-2.5
y=5 sin 60�=5*√3/2=5√3/2=4.33
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slope of line=1/√3 (negative reciprocal of perpendicular)
Equation: y=x/√3+b
solving for b, using point of intersection (x,y) coordinates
4.33=-2.5/√3+b
b=4.33+2.5/√3=4.33+1.44=5.77
equation of line:
y=x/√3+5.77
see graph below as a visual check on the answer
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