Question

use the law of sines to solve for b. use algebra to isolate b. \\(\frac{\sin(62)}{6} = \frac{\sin(69)}{b}\\) \\(b = \frac{?\sin(\quad)}{\sin(\quad)}\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{\sin(62^{\circ})}{6}=\frac{\sin(69^{\circ})}{b}\), cross - multiplying (which means multiplying both sides by \(6b\)) gives us \(b\times\sin(62^{\circ}) = 6\times\sin(69^{\circ})\).

Step2: Isolate \(b\)

To isolate \(b\), we divide both sides of the equation \(b\times\sin(62^{\circ})=6\times\sin(69^{\circ})\) by \(\sin(62^{\circ})\). So, \(b = \frac{6\times\sin(69^{\circ})}{\sin(62^{\circ})}\).

Answer:

\(b=\frac{6\sin(69^{\circ})}{\sin(62^{\circ})}\) (So the first box is \(6\), the second box is \(69^{\circ}\), and the third box is \(62^{\circ}\))