The length of DC is :

1. 10 m

2. $10(\sqrt{3} + 1)$ m

3. 20 m

4. $10(\sqrt{3} - 1)$ m

We know that,

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

From figure,

In △ ABC,

⇒ tan 45° = $\dfrac{AB}{BC}$

⇒ $1 = \dfrac{10}{BC}$

⇒ BC = 10 m.

In △ ABD,

⇒ tan 30° = $\dfrac{AB}{BD}$

⇒ $\dfrac{1}{\sqrt{3}} = \dfrac{10}{BD}$

⇒ BD = $10\sqrt{3}$ m.

From figure,

DC = BD - BC = $10\sqrt{3} - 10 = 10(\sqrt{3} - 1)$ m.

Hence, Option 4 is the correct option.