Question

If a pole hm high casts a shadow √3/3 h meter long on the ground find the sun's elevation?

Answer 1

Solution :-

Length of the pole = h meters

Length of the shadow = (√3/3 ) * h meters

Let θ be the angle of sun's elevation

The ratio of length of pole and shadow is tan θ

⇒ tanθ = Lengths of the pole / Length of the shadow

$\implies \tan \theta = \dfrac{h}{ \dfrac{ \sqrt{3} }{3}h}$

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

$\implies \tan \theta =1 \times \dfrac{3}{ \sqrt{3} }$

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

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

$\implies \tan \theta = \tan60$

[ Because tan60 = √3 ]

$\implies \theta = 60$

Therefore 60° is the angle of sun's elevation.