In a $30-60-90$ special right triangle, which angle measures $60°$?

• A. The angle opposite the side of length $1$
• B. The angle opposite the hypotenuse
• C. The right angle
• D. The angle opposite the side of length $\sqrt{3}$

Answer: (D)

Verified step by step guidance

1. Recall the properties of a 30°-60°-90° special right triangle: the sides are in the ratio 1 : \sqrt{3} : 2, where 1 is opposite the 30° angle, \sqrt{3} is opposite the 60° angle, and 2 is the hypotenuse opposite the right angle.
2. Identify the side lengths and their corresponding angles based on the ratio: the shortest side (length 1) is opposite 30°, the side of length \sqrt{3} is opposite 60°, and the longest side (hypotenuse) of length 2 is opposite the 90° angle.
3. Given the side lengths, determine which angle corresponds to the side of length \sqrt{3}. According to the ratio, this side is opposite the 60° angle.
4. Confirm that the right angle is always 90°, opposite the hypotenuse, which is the longest side in the triangle.
5. Therefore, the angle measuring 60° is the one opposite the side of length \sqrt{3}.