Shortest ladder problem
You have a box of width A and height B that stands next to a wall. What is the length C of the shortest ladder that will reach over the box and touch the wall?
We write C as a function of X. Using similar triangles:
Y1= √
(X2+(BX/(X-A))2
Now we store values for A and B:
width of box→A
height of box→B
To minimize C, we take its derivative and set it equal to zero.
We use Solver and nderiv:
eqn:0=nDeriv(Y1,X,X)
We make a guess for X and press alpha SOLVE.
To find the length of the ladder, from the home screen we press Y1.
Now you may check this by making a length C and trying it with your box!
Calculus Index