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

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 \( \sqrt{3} \).