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 \\(m \angle a = 30^{\circ}\\). what is the measure of angle b? \\(\bigcirc\\) \\(15^{\circ}\\) \\(\bigcirc\\) \\(30^{\circ}\\) \\(\bigcirc\\) \\(45^{\circ}\\) \\(\bigcirc\\) \\(60^{\circ}\\)

Explanation:

Step1: Apply Law of Sines ratio

$\frac{\sin(A)}{a} = \frac{\sin(B)}{b}$

Step2: Substitute given values

$\frac{\sin(30^\circ)}{2} = \frac{\sin(B)}{2}$

Step3: Simplify to solve for $\sin(B)$

Multiply both sides by 2: $\sin(B) = \sin(30^\circ)$

Step4: Find $\angle B$

Since $\sin(B)=\sin(30^\circ)$ and $a=b$, $\angle B = 30^\circ$

Answer:

30°