Question

Shadow of a vertical pillar is equal to the height of the pillar then the angle of elevation of sun will be :

• A. ${90}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

The correct option is C ${45}^o$

In right angle Δ$ABC,$ $AB$ represents the vertical pole and $BC$ represents the shadow on the ground.

$\theta$ represents angle of elevation the sun.

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

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

$\tan \theta =\frac{h}{h}=1$

$\tan \theta =\tan 45°$

$\theta =45°$

Thus, angle of elevation of the sun $=45°.$