PROBLEM:
A ladder 5m long leans against a wall reaching over the top of a box
that is 1m on each side. The box is against the wall. What is the maximum
height on the wall that the ladder can reach? Assume the wall is perpendicular
to the floor. Use your calculator to find the maximum height to the nearest
.01m.
By similar triangles, we know that
.Using the Pythagorean Theorem, we get the following:
Now, we need to graph this equation to find the maxium height on the
wall that the ladder can reach.
So, x = -5.95, -0.2, 0.25, or 3.85.
Now, we need to see which of these values for x will give us the maximum
y. We know that
.Therefore, the smallest positive value of x will give us our maximum
y.
Hence, the maximum distance the ladder can reach on the wall is 4 + 1
= 5 meters.