Question

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

Answer 1

`x = \sqrt 6`

Explanation:

Given

The attached triangle

Required

Find x

Considering angle 30 degrees,

`Opposite = \sqrt{2`

`Adjacent = x`

Using the tangent formula:

`tan\ 30 = (\sqrt 2)/(x)`

Make x the subject

`x = (\sqrt 2)/(tan\ 30)`

`x = (\sqrt 2)/(1/\sqrt 3)`

`x = \sqrt 2 * \sqrt 3`

`x = \sqrt 6`