Question

In triangle ABC, the length side c is 16, and the m∠A=30°. Find the exact lengths of a and b.
"Exact length" means leaving your answers in radical form, not rounded decimal ones. answer in 1-2 sentences

Answer 1

In triangle ABC, using the Law of Sines, we have \( \frac{a}{\sin A} = \frac{c}{\sin C} \) and the fact that \( A = 30^\circ \) and \( c = 16 \). Thus, \( a = \frac{16 \sin 30^\circ}{\sin C} = \frac{16 \cdot \frac{1}{2}}{\sin C} = \frac{8}{\sin C} \). To find b, we use \( \frac{b}{\sin B} = \frac{c}{\sin C} \) or \( b = \frac{16 \sin B}{\sin C} \), but we'll need the angle B; therefore, \( b \) and \( C \) will depend on how you choose angle B, necessitating further information for exact values.