Question

question 12 of 25 which proportion could be used to find the length of side b? a. $\frac{sin64}{b}=\frac{sin85}{a}$ b. $\frac{sin31}{9.3}=\frac{sin64}{b}$ c. $\frac{sin64}{9.3}=\frac{sin85}{b}$ d. $\frac{sin31}{9.3}=\frac{sin85}{b}$

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is $180^{\circ}$. So the third angle $C = 180-(64 + 85)=31^{\circ}$.

Step2: Apply the Law of Sines

The Law of Sines states that $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$. Here, side opposite $A = 9.3$, angle $A = 31^{\circ}$, angle opposite side $b$ is $64^{\circ}$. So $\frac{\sin31}{9.3}=\frac{\sin64}{b}$.

Answer:

B. $\frac{\sin31}{9.3}=\frac{\sin64}{b}$