Question

The triangle below is equilateral. Find the length of side 2 in simplest radical form
with a rational denominator.
x
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Answer: 2
attempt 1 out of 2
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Answer 1

Answer:

$x=\frac{4\sqrt{3}}{3}$

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

$\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}$

$\sqrt{3}=\frac{4}{x}$

$x=\frac{4}{\sqrt{3}}$

$x=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3} }$

$x=\frac{4\sqrt{3}}{3}$