Question

law of sines (\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c})
triangle (abc) has measures (a = 2), (b = 2), and (mangle a=30^{circ}). what is the measure of angle (b)?

Explanation:

Step1: Apply the Law of Sines

Given \(\frac{\sin(A)}{a}=\frac{\sin(B)}{b}\), substitute \(a = 2\), \(b = 2\), and \(A=30^{\circ}\). So \(\frac{\sin(30^{\circ})}{2}=\frac{\sin(B)}{2}\).

Step2: Simplify the equation

Since the denominators are equal (\(a = b = 2\)), then \(\sin(A)=\sin(B)\). Substituting \(\sin(30^{\circ})=\frac{1}{2}\), we get \(\sin(B)=\frac{1}{2}\). Also, because \(a = b\), by the property of triangles (sides opposite equal angles are equal), \(A = B\).

Answer:

\(30^{\circ}\)