Question

The measure of x is ______.

Options

• \(15 \sqrt{3} \mathrm{~cm}\)

• 15 cm

• \(5 \sqrt{3} \mathrm{~cm}\)

• 5 cm

Answer 1

The measure of x is \(\underline{\boldsymbol{5 \sqrt{3} \mathrm{~cm}}}\). 

Explanation: 

We know that,

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

From figure,

In \[\triangle ABC,\]

\[\Rightarrow \tan 60^\circ = \frac{AB}{BC}\]

\[\Rightarrow \sqrt{3} = \frac{15}{x}\]

\[\Rightarrow x = \frac{15}{\sqrt{3}}\]

Rationalizing the denominator,

\[\Rightarrow x = \frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\]

\[\Rightarrow x = \frac{15\sqrt{3}}{3}\]

\[\Rightarrow x = 5\sqrt{3}.\]