A vertical post of height h m rises from a plane which slopes down towards the South at an angle α to the horizontal. Prove that the length of its shadow when the sun is S𝛉W at an elevation β is ((h(√((1+tan^2 α cos^2 θ) )))/(tanβ + tanα cos θ))m


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Question Number 115642 by 24224 Opiyo Kamuki last updated on 27/Sep/20

$A v e r t i c a l p o s t o f h e i g h t h m r i s e s f r o m a p l a n e w h i c h$ $s l o p e s d o w n t o w a r d s t h e S o u t h a t a n a n g l e$ $α t o t h e h o r i z o n t a l . P r o v e t h a t t h e l e n g t h$ $o f i t s s h a d o w w h e n t h e s u n i s S θ W$ $a t a n e l e v a t i o n β i s$ $\frac{h \sqrt{(1 + {t a n}^{2} α {c o s}^{2} θ)}}{t a n β + t a n α \cos θ} m$
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