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∠a = 30°. what is the measure of angle b?
15°
30°
45°
60°

Explanation:

Step1: Apply the law of sines

According to the law of sines $\frac{\sin(A)}{a}=\frac{\sin(B)}{b}$. We know that $a = 2$, $b = 2$ and $A=30^{\circ}$. Substitute these values into the formula: $\frac{\sin(30^{\circ})}{2}=\frac{\sin(B)}{2}$.

Step2: Solve for $\sin(B)$

Cross - multiply the equation $\frac{\sin(30^{\circ})}{2}=\frac{\sin(B)}{2}$, we get $2\sin(B)=2\sin(30^{\circ})$. Since $\sin(30^{\circ})=\frac{1}{2}$, then $2\sin(B)=2\times\frac{1}{2}=1$, so $\sin(B)=\frac{1}{2}$.

Step3: Find the angle $B$

Since $0^{\circ}

Answer:

B. $30^{\circ}$