Question 593657: Find the angle (in degrees) between the two lines:
6x-y+8=0
-3x-11y+10=0 Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Find the angle (in degrees) between the two lines:
6x-y+8=0
-3x-11y+10=0
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Find the slope of each:
6x-y+8=0
m1 = 6
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-3x-11y+10=0
m2 = -3/11
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The tangent of the angle between the x-axis and the line is the slope.
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tan(A) = 6
A =~ 80.54 degs
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tan(B) = -3/11
B = -15.26 degs
diff = 96.8 degs
or 180 - 96.8 = 83.2 degs
The correct answer is 84.2° not 83.2°.
The other tutor used a different method from the usual method but he
also made an error in finding the angle of the second line. He erroneously
used the calculator negative result of tan-1() = -15.2551187,
which is the wrong angle. That is the 4th quadrant principle value of the
inverse tangent, not the 2nd quadrant angle which the second line makes with
the x-axis.
He should have gotten the reference angle by finding tan-1() = 15.255118.
Then he should have subtracted that from 180° to get the correct 2nd
quadrant angle, 164.7448813°
Then when he subtracted the angles he would have gotten
164.7448813° - 80.53767779° = 84.20729351°
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Here is the normal method for finding the angle between two
lines given their equations:
The formula for the tangent of the angle between two lines is:
tan(Ɵ) =
Find the slopes of the two lines, as the other tutor did.
6x - y + 8 = 0
-y = -6x - 8
y = 6x + 8
Compare to
y = mx + b
Slope = m = 6
We will call that m1
-3x - 11y + 10 = 0
-11y = 3x - 10
y = x +
Compare to
y = mx + b
Slope = m =
We will call that m2
tan(Ɵ) = = = = -9.857142867
Ɵ = 84.2072935°
Edwin
