Question

At a certain instant, the altitude of the sum is 60°. At that instant, the length of the shadow of a vertical tower is 100 m. The height of the tower is

(a) $50\sqrt{3}\mathrm{m}$
(b) $100\sqrt{3}\mathrm{m}$
(c) $\frac{100}{\sqrt{3}}\mathrm{m}$
(d) $\frac{200}{\sqrt{3}}\mathrm{m}$

Answer 1

(b) $100\sqrt{3}\mathrm{m}$
Let $AB$ be the tower and $AC$ be its shadow.
We have:
∠$ACB={60}^o$ and $AC=100$ m

Let:
$AB=h$ m
In the right ∆$BAC$, we have:
$\frac{AB}{AC}=\tan {60}^o=\sqrt{3}$

⇒ $\frac{h}{100}=\sqrt{3}$
⇒ $h=100\sqrt{3}$ m

Hence, the height of the tower is $100\sqrt{3}$ m.