This is a very challenging problem. I've been working on this for a while. (it was a word document at first).
Thanks. Any help is greatly appreciated
The first thing to do is give names to some of the unlabeled distances in the picture. Lets call the height of the short ladder and the height of the long one . We can also divide into two parts where it intersects the dotted red line; call the one on the left and the one on the right .
Now we have two pairs of similar right triangles; each ladder forms a triangle with the building and with the dotted red line. We can set up some proportions for these triangles:
By multiplying both sides of each equation by and seeing that we have
which after dividing both sides by becomes
Now all we have to do is use the Pythagorean Theorum to get and a similar expression for and substitute.
The easiest way to do part b is to plug in 12 for , then simplify the left side before taking the reciprocal of each side.
Part c is basically guess and check; use a calculator or computer program to plug lots of two-decimal-place values into that expression until you can change the sign by changing the plugged in value by only .01.