sin(30)/A=sin(30)/b = sin(120)/22
To find the value of \( b \), we can use the fact that the sine of an angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the hypotenuse.
Given:
\[
\frac{\sin(30^\circ)}{a} = \frac{\sin(30^\circ)}{b} = \frac{\sin(120^\circ)}{22}
\]
We know that \(\sin(30^\circ) = \frac{1}{2}\) and \(\sin(120^\circ) = \frac{\sqrt{3}}{2}\).
So, we have:
\[
\frac{\frac{1}{2}}{a} = \frac{\frac{1}{2}}{b} = \frac{\frac{\sqrt{3}}{2}}{22}
\]
Solving for \( b \), we get:
\[
\frac{\frac{1}{2}}{b} = \frac{\frac{\sqrt{3}}{2}}{22}
\]
\[
\frac{1}{2b} = \frac{\sqrt{3}}{44}
\]
\[
b = \frac{44}{2\sqrt{3}}
\]
\[
b = \frac{22}{\sqrt{3}}
\]
\[
b = \frac{22\sqrt{3}}{3}
\]
Thus, the value of \( b \) is \( \frac{22\sqrt{3}}{3} \).