SOLUTION: find the acute angle between the following straight lines y=(0.5)(x)+1 and y=-(1/3)(x)+2

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Question 1083349: find the acute angle between the following straight lines
y=(0.5)(x)+1 and y=-(1/3)(x)+2
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the angle is 45 degrees as best i can see.

i believe you can just go by the slope.

the y-intercept determines where the intersection of the 2 lines will be but it doesn't change the angle between the lines.

i tested this out and it appears to be correct.

a slope of .5 means the opposite side of the right triangle formed is 1/2 the length of the adjacent side.

if the adjacent side is equal to 1, then the opposite side is equal to 1/2 and the tangent of the angle is equal to 1/2 / 1 which is equal to 1/2 which gives you an angle of 26.56505118 when you find the arc tangent of 1/2.

a slope of -1/3 means the opposite side is 1/3 the length of the adjacent side.

if the adjacent side is equal to 1, then the opposite side is equal to -1/3 and the tangent of the angle is equal to -1/3 / 1 which gives you an angle of -18.43494882 degrees.

add these angles together and you get an angle of 45 degrees between the two lines.

these are vertical angles of the intersection.

the other vertical angles of the intersection will be 180 - 45 = 135 degrees.

45 degrees are the acute vertical angles.

135 degrees are the obtuse vertical angles.

the graph of these two lines looks like this.