Four students each select three pieces labeled with side lengths and angle measures: Don chooses $a=7$, $A=30°$, $B=60°$; Margo chooses $a=5$, $A=100°$, $b=2$; Sonji chooses $a=8$, $A=45°$, $b=6$; Liam chooses $a=3$, $A=80°$, $b=5$. According to the Law of Sines, which student chose pieces that can be used to construct a triangle?

• A. Liam
• B. Sonji
• C. Margo
• D. Don

Answer: (A)

Verified step by step guidance

1. Recall the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B}\), where \(a\) and \(b\) are sides opposite angles \(A\) and \(B\) respectively.
2. For each student, check if the given sides and angles satisfy the Law of Sines by calculating \(\frac{a}{\sin A}\) and \(\frac{b}{\sin B}\) and comparing these values.
3. Calculate \(\sin A\) and \(\sin B\) for each student using their given angle measures (in degrees), remembering to convert degrees to radians if necessary or use a calculator set to degrees.
4. Verify if the ratios \(\frac{a}{\sin A}\) and \(\frac{b}{\sin B}\) are approximately equal for each student; if they are, the pieces can form a triangle according to the Law of Sines.
5. Identify which students have consistent ratios, indicating their pieces can construct a triangle, and which do not, indicating no valid triangle can be formed.