Question

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

Answer 1

Answer:

$x = \frac{2*\sqrt{3}}{3}$

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

$tan (30) = \frac{opp}{adj}$

$tan (30) = \frac{x}{2}$

$2 * tan (30) = x$

$2 * \frac{1}{sqrt{3}} = x$ (tan 30 = 1/√3)

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

Rationalize

$\frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x$

$\frac{2*\sqrt{3}}{3} = x$