According to the information given in the following figure, the length of BC is :

1. $\sqrt{3}$ m

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

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

4. $2\sqrt{3}$ m

We know that,

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

From figure,

In △ ABD,

⇒ tan 45° = $\dfrac{AD}{BD}$

⇒ $1 = \dfrac{1}{BD}$

⇒ BD = 1 m.

In △ ACD,

⇒ tan 30° = $\dfrac{AD}{CD}$

⇒ $\dfrac{1}{\sqrt{3}} = \dfrac{1}{CD}$

⇒ CD = $\sqrt{3}$ m.

From figure,

BC = BD + CD = $(1 + \sqrt{3})$ m.

Hence, Option 3 is the correct option.