Question

The ratio of the length of a vertical rod and the length of its shadow is `1 : sqrt(3)`. What is the angle of elevation of the sun at that moment?

Answer 1

Given: The lengths of the vertical rod and its shadow are in the ratio `1 : sqrt(3)`.

Let the rod's height = h and shadow = `sqrt(3) xx h`. 

For angle of elevation θ,

`tan θ = "height"/"shadow"`

= `h/(sqrt(3) xx h)`

= `1/sqrt(3)` 

So `θ = arctan(1/sqrt(3))` = 30°.

The angle of elevation of the sun is 30°.