Need help with a math problem.

>>211293

If you know that the line is 33 units long use that to know the y and x on the right image. Then make the rotation point the origin and parametrize the extremes accordingly, break the problem into two triangles, one above the new origin and one below. Then see what information you can gather from those triangles and if the problem can be solved there should be some kind of consistency between something something. I'm too lazy to do it, tell me if it works or whatever.

>>211293
well let's number the point at the origin 0 and the point at (0,33) 1, to write down the new coordinates as a function of Y and θ (height of center of rotation and angle of rotation) you need to translate the whole line so (0,Y) maps to (0,0), perform the rotation (by multiplying a rotation matrix with the original points) and translate it back. eventually you'll get that
x0(Y,θ) = - (0 - Y) sin(θ)
y0(Y,θ) = (0 - Y) cos(θ) + Y
x1(Y,θ) = - (33 - Y) sin(θ)
y1(Y,θ) = (33 - Y) cos(θ) + Y
or more generally, if we parameterize the original line by {x = 0; y = 33t} where t = 0 corresponds to the first point and t = 1 to the second
x(t,Y,θ) = - (t - Y) sin(θ)
y(t,Y,θ) = (t - Y)cos(θ) + Y

anyway the system of equations you need to solve is
- (33 - Y) * sin(θ) = -11
Y * [1 - cos(θ)] = 8
one possible solution for this is roughly θ = 2.75 rads and Y = 4.175, and I suspect existence of another solution but am too lazy to check.

>>211364
oops, meant to write
x(t,Y,θ) = - (33t - Y) sin(θ)
y(t,Y,θ) = (33t - Y)cos(θ) + Y

here's some desmos widget to play around with. https://www.desmos.com/calculator/mc5qvbxyn9

>>211368
and another one if you don't want the second point to be lower than the first θ = 0.943 rads (54 degs) and Y = 19.387

>>211293
You can do it with elementary math, just draw both segments in the same coordinate system with a rotation point A=(0,a).

If you draw segments parallel to the x-axis from the new end points to the old segment (= the y axis) you see that you get two similar triangles (the three angles are equal).

The two hypothenuses are a and 33-a, two corresponding sides are 8 and 11.

Since the triangles are similar, you obtain

a/8 = (33-a)/11
19a = 264
a = 264/19 ~ 13.9

>>211293
find the point of intersection of both lines

>>211398
are you plain retarded or just pretending