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

Answer

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Answer

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

Steps

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 ：\( \sin x^{\circ} = \frac{a}{b} \)