Question

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

Options

• \[\sqrt{3} \mathrm{~m}\]

• \[(\sqrt{3}-1) \mathrm{m}\]

• \[(\sqrt{3}+1) \mathrm{m}\]

• \[2 \sqrt{3} \mathrm{~m}\]

Answer 1

\[\boldsymbol{(\sqrt{3}+1) \mathrm{m}}\]

Explanation:

We know that,

\[\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}\]

From figure,

In \[\triangle ABD,\]

\[\Rightarrow \tan 45^\circ = \frac{AD}{BD}\]

\[\Rightarrow 1 = \frac{1}{BD}\]

\[\Rightarrow BD = 1\ \text{m}.\]

In \[\triangle ACD,\]

\[\Rightarrow \tan 30^\circ = \frac{AD}{CD}\]

\[\Rightarrow \frac{1}{\sqrt{3}} = \frac{1}{CD}\]

\[\Rightarrow CD = \sqrt{3}\ \text{m}.\]

From figure,

\[BC = BD + CD = (1 + \sqrt{3})\ \text{m}.\]