Question

Find the angle of elevation of the sun (suns altitude) when the length of the shadow of a vertical pole is equal to its height.

Answer 1

In right angled $△ABC,$ $AB$ represents the vertical tower and $BC$ represents the shadow. $\theta$ represents the elevation angle of the sun.

$\Rightarrow$ $\tan \theta =\frac{AB}{BC}$

$\Rightarrow$ $\tan \theta =\frac{h}{x}$

But length of shadow = Height of the tower, i.e $h=x.$

$\therefore$ $\tan \theta =\frac{h}{h}$

$\Rightarrow$ $\tan \theta =1$

$\therefore$ $\theta ={\tan }^{-1}\left(1\right)$

$\therefore$ $\theta ={45}^o$

Thus, elevation angle of sun is ${45}^o$.