Answer:
D. √3
Explanation:
- This is a 30-60-90 triangle that has special rules concerning its side lengths.
- Let's call the length of the side opposite the 30° angle a.
- The length of the side opposite the 60° angle is a * √3.
- The length of the 90° (right) angle is 2a.
The tangent ratio is given by:
tan (θ) = opposite/adjacent, where
- θ is the reference angle.
- When the 60° angle is the reference angle, the side that is 8 * √3 units long is the opposite side.
- The side with an unknown length and opposite the 30° angle is the adjacent side.
- According to the 30-60-90 triangle rules, 8 is a and this is the length of the side opposite the 30° angle.
Thus, we plug in 8√3 for the opposite side and 8 for the adjacent side, which gives us:
tan (60) = (8√3) / 8
Thus reduces down to √3 so D. is the correct answer.