Question

A pole 6 m high casts a shadow $2\sqrt{3}\mathrm{m}$ long on the ground. At that instant, the sun's elevation is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer 1

(c) 60°
Let $AB$ be the pole and $AC$ be its shadow.
Let ∠$ACB=\theta$, $AB=6$ m and $AC=2\sqrt{3}$ m.

In ∆$ACB$, we have:

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

⇒ $\frac{6}{2\sqrt{3}}=\tan \theta$

⇒ $\tan \theta =\sqrt{3}$
⇒ $\theta ={60}^o$

Hence, the angle of elevation of the sun is 60°.