SOLUTION: Find the smallest angle between the lines 2x + y = 0 and x + 3y + 4 = 0

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Question 948934: Find the smallest angle between the lines 2x + y = 0 and
x + 3y + 4 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the angle each line makes with the x-axis.
2x%2By=0
y=-2x
m%5B1%5D=-2
Slope is change in y over change in x.
So then the angle is,
tan%28alpha%29=m
tan%28alpha%29=-2
alpha=-63.4
.
.
.
x%2B3y%2B4=0
3y=-x-4
y=-x%2F3-4%2F3
m%5B2%5D=-1%2F3
tan%28beta%29=-1%2F3
beta=-18.4
Now find the difference between the two angles, that's the angle between them,
theta=beta-alpha
theta=-18.4-%28-63.4%29=highlight%2845%29