Question

A 20 foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building what angle does the ladder make with the ground

Answer 1

$From \:the \: rough \: figure, \\Length \:of \:the \:ladder (AC) = 20 \:ft$

$Distance \:from \: foot \:of \:the ladder \:to \\base \: of \:the \: building = 8 \:ft$

$Let \angle {BAC } = \theta$

$In \: \triangle ABC , \: \angle {ABC} = 90\degree$

$Cos\: \theta = \frac{AB}{AC} \\= \frac{8}{20} \\= \frac{2}{5}$

$\implies \theta = cos^{-1} \big(\frac{2}{5}\big)$

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