the base of the ladder sliding down the wall
Perhaps, you mispoke? The base of the ladder is sliding along the floor -- away from the wall.
The top of the ladder is sliding down the wall.
Really, I think that we may freeze time, and just consider the triangle formed at that instant as representative of all the triangles.
Your method is a bit confusing.
I posted no method.
I posted some clues that I hoped would get you thinking.
learning about parametric equations
I fail to see how this problem quite relates to the subject matter.
Ah, thank you for reminding me that you asked for an explanation of the exercise. You may always feel free to do that.
We assume that the bottom of the ladder does not sway to the left or right, but moves in a straight line away from the wall. Hence, point P moves within the plane that contains the ladder, and so we can describe the location of point P using an xy-coordinate system with a line segment representing the ladder. Point P will trace out a curved path, from start to finish.
For example, before the ladder moves, point P is located at (0,11). Do you agree? Likewise, when the ladder stops moving, the location of point P will be (5,0).
We may describe the path of point P with a system of two equations. Each equation will be a function definition, and these functions' input will be the measure of angle theta in radians (a Real number).
The output of the first function will be the x-coordinate of point P, for any given Real number theta within the domain.
The output of the second function will be the y-coordinate of point P, for the same Real number theta.
x(θ) = some expression containing θ
y(θ) = some expression containing θ
The two equations above are parametric equations. They give P's location (
x(θ),
y(θ)) in terms of the parameter theta. When plotted across the domain, the graph shows the path of P.
Do you remember Right-Triangle Trigonometry? Can you determine what the value of θ is before the ladder moves? When the ladder stops moving, it is obvious what θ equals, yes? (These beginning and ending values define the domain of θ. Stating the domain is a required part of the system of parametric equations, so you should report it.)
Have you drawn a diagram, yet? Do you understand how to draw a representative triangle in Quadrant I? Do you understand how to connect P to the x-axis with a vertical line segment?
In order to attempt clearing up confusion, I first need to know exactly where the confusion lies.
Cheers :cool: