What is the length of the ladder?
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Step 1let the length of ladder be x feet\begin{array}{l}\angle A B C=75^{\circ} \\\angle A C B=90^{\circ} \\B C=6 \text { feet }\end{array}Step 2In right angled \triangle A B C\begin{aligned}& \cos \angle A B C=\frac{B C}{A B} \\\Rightarrow \cos 75 & =\frac{6}{x} \\\Rightarrow x & =\frac{6}{\cos 75} \\\Rightarrow x & =23.18 \text { fuet }\end{aligned}length of ladder =x=23.18 feet ...