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Delicious77 [7]
3 years ago
14

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

Mathematics
1 answer:
alekssr [168]3 years ago
4 0

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

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