A fence 6 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram.
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We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building.

[A] First, find a formula for the length of the ladder in terms of $\displaystyle \theta$. (Hint: split the ladder into 2 parts.)
Type theta for $\displaystyle \theta$.

$\displaystyle {L}{\left(\theta\right)}=$Preview Question 6 Part 1 of 3  

[B] Now, find the derivative, $\displaystyle {L}'{\left(\theta\right)}$.
Type theta for $\displaystyle \theta$.

$\displaystyle {L}'{\left(\theta\right)}=$Preview Question 6 Part 2 of 3  

[C] Once you find the value of $\displaystyle \theta$ that makes $\displaystyle {L}'{\left(\theta\right)}={0}$, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.)

$\displaystyle {L}{\left(\theta_{{\min}}\right)}\approx$ feet