Look at the figure: If \( \tan x^{\circ}=\frac{a}{4} \) and \( \cos x^{\circ}=\frac{4}{b} \) what is the value of \( \sin x^{\circ} ? \)

Step 1 ：\( \tan x^{\circ} = \frac{\sin x^{\circ}}{\cos x^{\circ}} \Rightarrow \sin x^{\circ} = \tan x^{\circ} \cos x^{\circ} \)

Step 2 ：\( \sin x^{\circ} = \left(\frac{a}{4} \right) \left(\frac{4}{b} \right) \)

Step 3 ：\( \sin x^{\circ} = \frac{a}{b} \)