What is the angle between slopes?
What is the measurement of the angles between the two lines and .
Round your answer to the nearest integer .
Note : You will receive two answers unless the angles are all 90 degrees (or radians).
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1 solution
EQUATION SHORT VERSION
(m2-m1)/(1+m2*m1) = tan(x)
(2-0)/(1+0) = tan(x)
2/1 = tan(x)
arctan(2) = 1.10714872 rad = 63.434948949468676 degrees
round 63.434948949468676 degrees to 63 degrees.
and the other angle is obviously about 117 degrees.
UP AND DOWN: 117 degrees
LEFT AND RIGHT: 63 degrees
TRIG LONG VERSION
With a bit of trigonometry we can solve this easily.
(but fairly more difficult to do in the reverse to create a set of equations that isn't overly complicated)
1.First find the point of intersection,
2X=2.5
X=2.5
(^^so difficult^^)
input into either function.
You get the output of 5.
POINT OF INTERSECTION: (2.5,5)
2.Now pick two arbitrary points on the lines.
(I will do x of 1)
You get two more points at
(1,5) and (1,2)
3.Doing some quick law of cosines (C^2=A^2+B^2-2AB*cos(angle)) You get a right triangle(obvious from coordinates) with sides hypotenuse:sqrt(11.25) and legs: 1.5 and 3
4.SOHCAHTOA tells us what we must do.
(I will use tangent for now)
tan(x)=opposite/adjacent
We need the angle at the point of intersection so
tan(x)=3/1.5
tan(x)=2
arctan(2) = 1.10714872 rad
1.10714872 rad = 63.434948949468676 degrees
We round this to 63.
And we also know the other angle is 117. (the angles up and down are 117 the angles left and right are 63)