The length of DC is :

1. $45\sqrt{3}$ m

2. $(45 - \sqrt{3})$ m

3. $45(\sqrt{3} - 1)$ m

4. $45(\sqrt{3} + 1)$ m

We know that,

tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}}$

From figure,

In △ ABC,

⇒ tan 45° = $\dfrac{AB}{BC}$

⇒ $1 = \dfrac{AB}{45}$

⇒ AB = 45 m.

In △ ABD,

⇒ tan 30° = $\dfrac{AB}{BD}$

⇒ $\dfrac{1}{\sqrt{3}} = \dfrac{45}{BD}$

⇒ BD = $45\sqrt{3}$ m.

From figure,

DC = BD - BC = $45\sqrt{3} - 45 = 45(\sqrt{3} - 1)$ m.

Hence, Option 3 is the correct option.