Triangle $BCD$ is rotated $80°$ clockwise about the origin to form $KLM$. If $\angle KLM=30°$, what is the sine of angle $\angle KLM$?

• A. $1$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{2}$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Understand that rotating a triangle about the origin is a rigid transformation, which means the shape and size of the triangle, including its angles, remain unchanged.
2. Since triangle BCD is rotated 80° clockwise to form triangle KLM, the corresponding angles in triangle KLM are congruent to those in triangle BCD.
3. Given that angle \( \angle KLM = 30^\circ \), we want to find \( \sin(\angle KLM) \).
4. Recall the sine value for a 30° angle: \( \sin(30^\circ) = \frac{1}{2} \).
5. Therefore, the sine of angle \( \angle KLM \) is \( \frac{1}{2} \), since the rotation does not change the angle measure.