Question

if an a tower 30 m high casts a shadow 10√3 m long on the ground then what is the angle of elevation of the sun?​

Answer 1

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Solution :

$\implies \tan \theta = \frac{adjacent}{opposite}$

$\implies \tan \theta = \frac{10\sqrt{3} }{30}$

$\implies \tan \theta = \frac{\sqrt{3}}{3}$

$\implies \tan \theta = \frac{\sqrt{3} }{\sqrt{3} \times\sqrt{3} }$

$\implies \tan \theta = \frac{1}{\sqrt{3} }$

$\implies\tan \theta = 30°\:\:\:\:\:\: (\because \tan30° = \frac{1}{\sqrt{3} } )$

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Answer 2

height of tower = 30m = opposite side

Length of shadow = 10√3 = adjacent side

tan∅ = adjacent/opposite

tan∅ = 10√3/30

tan∅ = √3/3

tan∅ = 1/√3 = 30°