Question

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

Explanation:

Step1: Recall sine - law formula

The sine - law states that in a triangle \(ABC\), \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\).

Step2: Rearrange for \(b\)

Given \(A = 35^{\circ}\), \(B = 40^{\circ}\), and \(a = 9\), from \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we can cross - multiply to get \(\frac{\sin35^{\circ}}{9}=\frac{\sin40^{\circ}}{b}\).

Answer:

A. \(\frac{\sin35^{\circ}}{9}=\frac{\sin40^{\circ}}{b}\)