Question

The length of DC is ______.

Options

• \(45 \sqrt{3} \mathrm{~m}\)

• \((45-\sqrt{3}) \mathrm{m}\)

• \(45(\sqrt{3}-1) \mathrm{m}\)

• \(45(\sqrt{3}+1) \mathrm{m}\)

Answer 1

The length of DC is \(\underline{\boldsymbol{45(\sqrt{3}-1) \mathrm{m}}}\).

Explanation:

We know that,

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

From figure,

In △ ABC,

\[\Rightarrow \tan 45^\circ = \frac{AB}{BC}\]

\[\Rightarrow 1 = \frac{AB}{45}\]

⇒ AB = 45 m.

In △ ABD,

\[\Rightarrow \tan 30^\circ = \frac{AB}{BD}\]

\[\Rightarrow \frac{1}{\sqrt{3}} = \frac{45}{BD}\]

\[\Rightarrow BD = 45\sqrt{3}\ \text{m}.\]

From figure,

DC = BD − BC = \[45\sqrt{3} - 45 = 45(\sqrt{3} - 1)\ \text{m}.\]