Question

The length of AC is ______.

Options

• \((60-20 \sqrt{3}) \mathrm{m}\)

• \(60 \sqrt{3} \mathrm{~m}\)

• \((60+20 \sqrt{3}) \mathrm{m}\)

• \(20 \sqrt{3} \mathrm{~m}\)

Answer 1

The length of AC is \(\underline{\boldsymbol{(60+20 \sqrt{3}) \mathrm{m}}}\).

Explanation:

In rectangle BCDE,

Opposite sides of rectangle are equal.

\[\therefore BE = DC = 60\ \text{m}\]

We know that,

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

From figure,

In \[\triangle ABE,\]

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

\[\Rightarrow \frac{1}{\sqrt{3}} = \frac{AB}{60}\]

\[\Rightarrow AB = \frac{60}{\sqrt{3}} = 20\sqrt{3}\ \text{m}.\]

In \[\triangle EBC,\]

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

\[\Rightarrow 1 = \frac{BC}{60}\]

\[\Rightarrow BC = 60\ \text{m}.\]

From figure,

\[AC = AB + BC = (20\sqrt{3} + 60)\ \text{m}.\]