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

Find The Length Of Side X In Simplest Radical Form With A Rational Denominator class=

Sagot :

Akposevictoridn

Answer:

[tex] x = \frac{2*\sqrt{3}}{3} [/tex]

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

[tex] tan (30) = \frac{opp}{adj} [/tex]

[tex] tan (30) = \frac{x}{2} [/tex]

[tex] 2 * tan (30) = x [/tex]

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

[tex] \frac{2}{sqrt{3}} = x [/tex]

Rationalize

[tex] \frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x [/tex]

[tex] \frac{2*\sqrt{3}}{3} = x [/tex]

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