Question

Find the length of sides in simplest radical form with a rational denominator.

Answer 1

Given:

In a right angle triangle, two interior angles are 60° and 30°, and their opposite sides are x and 3 respectively.

To find:

The length of side x in simplest radical form with a rational denominator.

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

Using this formula for the given triangle, we get

$\tan 30^\circ=\dfrac{3}{x}$

$\dfrac{1}{\sqrt{3}}=\dfrac{3}{x}$

On cross multiplication, we get

$1\times x=3\times \sqrt{3}$

$x=3\sqrt{3}$

Therefore, the length of side x in simplest radical form is $3\sqrt{3}$ units.