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=(Perpendicular)/(Base)`

Using this formula for the given triangle, we get

`\tan 30^\circ=(3)/(x)`

`(1)/(√(3))=(3)/(x)`

On cross multiplication, we get

`1* x=3* √(3)`

`x=3√(3)`

Therefore, the length of side x in simplest radical form is
`3√(3)` units.