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Minimum length problem

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A fence 3√3 meters high stands 1 meter away from a wall. What is the shortest ladder that can reach from the fence to the wall? Hint: draw a picture. Let (theta) be the angle the ladder makes with the ground. Part of the ladder goes from the ground to the top of the fence, and the other part goes from the top of the fence to the wall, and the length of each part can be expressed in terms of (theta).

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Please refer to the attachment.

BE/EC = 1/x = cosθ or x = 1/cosθ

DE/EF = 3√3/y = sinθ or y = 3√3/sinθ

Length of the ladder = l = x + y = 1/cosθ + 3√3/sinθ = secθ + 3√3cosecθ ...

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