Question

question 11 of 40
in triangle abc, m∠a = 35°, m∠b = 40°, and a = 9. which equation should you solve to find b?
a. b² = 9² - 2(9)bcos40°
b. $\frac{sin35^{circ}}{9}=\frac{sin40^{circ}}{b}$
c. $\frac{cos35^{circ}}{9}=\frac{cos40^{circ}}{b}$
d. $\frac{sin35^{circ}}{b}=\frac{sin40^{circ}}{9}$

Explanation:

Step1: Recall the Law of Sines

The Law of Sines states that in a triangle $\triangle ABC$ with sides $a$, $b$, $c$ and opposite - angles $A$, $B$, $C$ respectively, $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$.

Step2: Identify given values

We are given that $A = 35^{\circ}$, $B = 40^{\circ}$, and $a = 9$. We want to find $b$.

Step3: Apply the Law of Sines

Substituting the given values into the Law - of - Sines formula $\frac{\sin A}{a}=\frac{\sin B}{b}$, we get $\frac{\sin35^{\circ}}{9}=\frac{\sin40^{\circ}}{b}$.

Answer:

B. $\frac{\sin35^{\circ}}{9}=\frac{\sin40^{\circ}}{b}$