QuestionWe 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 $\theta$. (Hint: split the ladder into 2 parts.) Type theta for $\theta$. $$L(\theta)=\frac{15}{\sin (\theta)}+\frac{5}{\cos (\theta)}$$ [B] Now, find the derivative, $L^{\prime}(\theta)$. Type theta for $\theta$. $$L^{\prime}(\theta)=-\frac{15 \cos (\theta)}{\sin ^{2}(\theta)}+\frac{5 \sin (\theta)}{\cos ^{2}(\theta)}$$ [C] Once you find the value of $\theta$ that makes $L^{\prime}(\theta)=0$, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) $$L\left(\theta_{\min }\right) \approx 1 \text { feet }$$ $\square$ Enter an integer or decimal number [more.-1] Submit Question