Question

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

Answer 1

Answer:

$x = \sqrt 6$

Step-by-step explanation:

Given

The attached triangle

Required

Find x

Considering angle 30 degrees,

$Opposite = \sqrt{2$

$Adjacent = x$

Using the tangent formula:

$tan\ 30 = \frac{\sqrt 2}{x}$

Make x the subject

$x = \frac{\sqrt 2}{tan\ 30}$

$x = \frac{\sqrt 2}{1/\sqrt 3}$

$x = \sqrt 2 * \sqrt 3$

$x = \sqrt 6$