Question

If the length of shadow a pole on a level ground is twice the length of the pole, the angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) none of these

Answer 1

(d) None of these

Let $AB$ be the pole and $AC$ be its shadow such that $AC=2AB$.
Let:
∠$ACB=\theta$

In ∆$ACB$, we have:

$\frac{AB}{AC}=\tan \theta$

⇒ $\frac{AB}{2AB}=\tan \theta$

⇒ $\tan \theta =\frac{1}{2}$
It is different from ${30}^o,{45}^o$ and ${60}^o$.