Web-Based Computational Tools Page 4 of 6

You will use Newton's method to help solve the following problem:

A 3 m ladder is leaning against the wall in a hallway so that its base is against the opposite wall. A 2 m ladder is leaning in a similar way, but against the other wall. From the side, the profiles of ladders intersect at a point 1 m from the floor. How wide is the hallway?

• Let w be the width of the hallway. Find an equation involving w that can be solved to give the desired width. (Hint: You could use the cotangent function several times.)

• What is a reasonable estimate for the width of the hallway?

• Use Newton's method in the MathServ Calculus Toolkit to solve your equation for w starting with your estimate from above.

When you are satisfied with your results, print this page and continue with the next.