SOLUTION: the perpendicular from the origin on a line makes and angle of 30 with y axis and its length is 2 units. Find the equation of the line.

Algebra ->  Points-lines-and-rays -> SOLUTION: the perpendicular from the origin on a line makes and angle of 30 with y axis and its length is 2 units. Find the equation of the line.      Log On


   

Question 1109264: the perpendicular from the origin on a line makes and angle of 30 with y axis and its length is 2 units. Find the equation of the line.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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From the diagram,
A%2B60%2B90=180
A=30
The relationship between the slope of the line and the angle it makes with the x axis, alpha, is,
m=tan%28alpha%29
m=tan%2830%29
m=sqrt%283%29%2F3
You cam find the x-intercept,
sin%2830%29=2%2FX
X=2%2F0.5
X=4
So,
0=%28sqrt%283%29%2F3%29%28-4%29%2Bb
b=%284%2F3%29sqrt%283%29
Finally,
y=%28sqrt%283%29%2F3%29x%2B%284%2F3%29sqrt%283%29