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= √
(X^{2}+(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