# Solving a Complex Math Problem: Real and Imaginary Solutions

• Noir

## Homework Statement

Apparantley the following problem can't be solved with a graphics calculator and we have to state why this is, and give all the possible solutions.

A ladder AB leans against the side of a building. Where the wall meets the ground is a cubic packing case 1m x 1m x 1m. The ladder is adjusted so that it rests on the ground, touches the packing case and rests against the wall. If the ladder is 10 metres long, how far up the wall will the ladder reach.

That was the question and a diagram was drawn, except I can't scan it in at the moment. Thinking on the problem there is more than one answer to the problem. Apparantley there are real and imaginary solutions.

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## The Attempt at a Solution

Using similar triange theroy, I get the following; x.y = 1.
Using pascals formula; 1^2 = (x + 1)^2 + (y + 1)6=^2
Solving the two equations gives an x value of -1.88 and a y value of -0.53.
Except I know I've made an mistake above and don't know how to continue. Can anyone help me please?