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orchidthief
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Homework Statement
Consider a large triangle, the tip is located at the origo x=0, it is sloped at an angle θ and -θ relative to the x-axis, relative to the x-axis, its dimensions in x can be considered infinite.
A large stripe/strip/band is placed on top of the triangle but perpendicular to the x-axis so to speak, it has a width b and it's center is located at x=0 and it can be considered infinite in the y direction. (So one edge of the stripe at the start is at x=b/2 and the other at x=-b/2.)
This large stripe can be shifted in the x direction to gradually cover a larger and larger trapezoidal area of the triangle.
The exercise is to find a generalised expression for the area shared by the triangle and the stripe as a function of x.2. The attempt at a solution
What I deduced was that this was a piecewise solution, while x<b/2 the area they share is:
A(x)= tanθ(x+b/2)^2 (a basic area of a triangle, that gives it an area when x=0)
And when x>b/2 it
A(x)=1/2*b*(q+p) (the area of a trapezoid)
Where q=2tanθ(x-b/2) and p=2tanθ(x+b/2) giving me a final expression in this part of:
A(x)=2bx*tanθ
Now my question is, the actual wording of the problem makes it sound like it should be possible to find one elegant expression covering the x>0 regardless of the zone, but I'm just completely lost in how one such might be found. Any help would be nice.
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