Finding the Shortest Ladder: Solving for the Optimal Angle

[alpha01]

Finding the "shortest ladder"

Problem

I was given an analogy involving a ladder that goes over a fence and then leans against a wall a meter after the fence. The question wanted me to answer "what is the shortest ladder that goes over the fence and reaches the wall"

The Attempt at a Solution

I worked out the equation of the "ladder" (i.e line from the ground to the wall) is:

(3sqrt(3) / sin x) + sec x

(where x is the angle the ladder makes with the ground and the wall)

How can i work out the "shortest" ladder that can be made to reach the wall. Is is simply the derivative of the ladder?

 

[Dick]

So 3sqrt(3) must be the height of the ladder h, right? Yes, the length of the ladder is L=h/sin(x)+1/cos(x). Differentiate that with respect to the angle, x, set it equal to zero and solve for x.