Jse a special right triangle to write $$ an 60^{\circ} $$ as a fraction. $$ \frac{\sqrt{3}}{2} $$ $$ \frac{\sqrt{3}}{\frac{\sqrt{3}}{3}} $$ 1

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Jse a special right triangle to write $$ 	an 60^{\circ} $$ as a fraction. $$ \frac{\sqrt{3}}{2} $$ $$ \frac{\sqrt{3}}{\frac{\sqrt{3}}{3}} $$ 1

UpStudy AI · Accepted Answer

To find $$ \tan 60^{\circ} $$ using a special right triangle, we can use the properties of a 30-60-90 triangle.

### Step 1: Understand the 30-60-90 Triangle
In a 30-60-90 triangle, the sides are in the ratio:
- Opposite the 30° angle: $$ x $$
- Opposite the 60° angle: $$ x\sqrt{3} $$
- Hypotenuse: $$ 2x $$

### Step 2: Identify the Sides
Let's assign $$ x = 1 $$ for simplicity:
- Opposite the 30° angle: $$ 1 $$
- Opposite the 60° angle: $$ 1\sqrt{3} = \sqrt{3} $$
- Hypotenuse: $$ 2 $$

### Step 3: Calculate $$ \tan 60^{\circ} $$
The tangent function is defined as the ratio of the opposite side to the adjacent side. For $$ 60^{\circ} $$:
$$
\tan 60^{\circ} = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\sqrt{3}}{1} = \sqrt{3}
$$

### Step 4: Write as a Fraction
To express $$ \tan 60^{\circ} $$ as a fraction, we can write:
$$
\tan 60^{\circ} = \frac{\sqrt{3}}{1}
$$

### Conclusion
Thus, $$ \tan 60^{\circ} $$ as a fraction is:
$$
\sqrt{3}
$$

The options provided in the question do not directly represent $$ \tan 60^{\circ} $$ as a fraction. However, the correct value is $$ \sqrt{3} $$.
$$ \tan 60^{\circ} = \sqrt{3} $$

Jse a special right triangle to write as a fraction.

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Jse a special right triangle to write as a fraction. 1