Question

what is the angle of elevation of the sun when the length of the shadow of the pole is 1/√3 times the height of the pole????

Answer 1

$\text{Let the angle of elevation = } \theta$

the length of the shadow of the pole is 1/√3 times the height of the pole.

$\text{Let the height = h} \\ \\ \text{length of shadow(s) = } \frac{1}{ \sqrt{3} } \times h = \frac{h}{ \sqrt{3} }$

$\text{from diagram}\\ \\ \tan( \theta) = \frac{h}{s} \\ \\ \tan( \theta) = \frac{h}{ \frac{h}{ \sqrt{3} } } \\ \\ \tan( \theta) = h \times \frac{ \sqrt{3} }{h} \\ \\ \tan( \theta) = \sqrt{3} \\ \\ \tan( \theta) = \tan( {60}^{o} ) \\ \\ \theta = {60}^{o} \\ \\ \boxed{ \large \text{angle \: of \: elevation \: is \:} {60}^{o} }$

Answer 2

I hope it help's u......