The measure of x is :

1. $15\sqrt{3}$ cm

2. 15 cm

3. $5\sqrt{3}$ cm

4. 5 cm

We know that,

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

From figure,

In △ ABC,

⇒ tan 60° = $\dfrac{AB}{BC}$

⇒ $\sqrt{3} = \dfrac{15}{x}$

⇒ x = $\dfrac{15}{\sqrt{3}}$

Rationalizing the denominator,

$\Rightarrow x = \dfrac{15}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} \\[1em] \Rightarrow x = \dfrac{15\sqrt{3}}{3} \\[1em] \Rightarrow x = 5\sqrt{3}.$

Hence, Option 3 is the correct option.