In triangle $LNP$, the length of side $LN$ is $28$ centimeters. If angle $P$ is $30°$ and angle $N$ is $60°$, what is the length of side $LP$?

• A. $28$ centimeters
• B. $24$ centimeters
• C. $16$ centimeters
• D. $14$ centimeters

Answer: (D)

Verified step by step guidance

1. Identify the given elements in triangle LNP: side LN = 28 cm, angle P = 30°, and angle N = 60°.
2. Calculate the remaining angle L using the triangle angle sum property: \(\angle L = 180^\circ - \angle N - \angle P\).
3. Use the Law of Sines, which states \(\frac{\text{side opposite to } \angle L}{\sin(\angle L)} = \frac{\text{side opposite to } \angle N}{\sin(\angle N)} = \frac{\text{side opposite to } \angle P}{\sin(\angle P)}\).
4. Set up the ratio using the known side LN (opposite angle P) and the side LP (opposite angle N): \(\frac{LN}{\sin(\angle P)} = \frac{LP}{\sin(\angle N)}\).
5. Rearrange the equation to solve for LP: \(LP = LN \times \frac{\sin(\angle N)}{\sin(\angle P)}\).