Using the information given in the following figure, the measurement of AE is :

1. 20 cm

2. 10 cm

3. $6\dfrac{2}{3}$ cm

4. $20\sqrt{3}$ cm

We know that,

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

From figure,

In △ ABC,

⇒ tan 60° = $\dfrac{AB}{BC}$

⇒ $\sqrt{3} = \dfrac{20}{BC}$

⇒ BC = $\dfrac{20}{\sqrt{3}}$ cm.

In rectangle BCDE,

Opposite sides of rectangle are equal.

∴ DE = BC = $\dfrac{20}{\sqrt{3}}$ cm

From figure,

In △ AED,

⇒ tan 30° = $\dfrac{AE}{DE}$

⇒ $\dfrac{1}{\sqrt{3}} = \dfrac{AE}{\dfrac{20}{\sqrt{3}}}$

⇒ AE = $\dfrac{1}{\sqrt{3}} \times \dfrac{20}{\sqrt{3}} = \dfrac{20}{3} = 6\dfrac{2}{3}$ cm.

Hence, Option 3 is the correct option.