Question

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

Answer 1

`x = (2*√(3))/(3)`

Explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

`tan (30) = (opp)/(adj)`

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

`2 * tan (30) = x`

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

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

Rationalize

`\frac{2* √(3)}{sqrt{3} * √(3)} = x`

`(2*√(3))/(3) = x`