SOLUTION: Q) Find the angle θ (in radians and degrees) between the lines. Round to three decimal places, if necessary. 6x + 2y = 9 –5x + 6y = 4

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Q) Find the angle θ (in radians and degrees) between the lines. Round to three decimal places, if necessary. 6x + 2y = 9 –5x + 6y = 4      Log On


   



Question 329030: Q) Find the angle θ (in radians and degrees) between the lines. Round to three decimal places, if necessary.
6x + 2y = 9
–5x + 6y = 4

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The angle that the line makes with respect to the y axis has a relationship to the line.
The tangent of the angle is equal to the change in y divided by the change in x using trigonmetry.
But the change in y over the change in x is also the slope of the line.
m=tan%28theta%29
Convert both lines to slope intercept form and find their slopes.
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6x+%2B+2y+=+9
2y=-6x%2B9
y=-3x%2B9%2F2
m1=tan%28alpha%29=-3
alpha=1.893radians
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-5x+%2B+6y+=+4
6y=5x%2B4
y=%285%2F6%29x%2B2%2F3
m2=tan%28beta%29=5%2F6
beta=0.695radians
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The angle between them X is then
X=1.893-0.695=1.199radians
X=1.199%28360%2F2pi%29=68.629degrees
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