Given:
[tex]\begin{gathered} tan\text{ x = }\frac{a}{4} \\ cos\text{ x= }\frac{4}{b} \end{gathered}[/tex]
Recall that for a right-angled triangle, the following trigonometric ratios are defined
[tex]\begin{gathered} sin\text{ }\theta\text{ = }\frac{opposite}{hypothenuse} \\ cos\text{ }\theta\text{ = }\frac{adjacent}{hypothenuse} \\ tan\theta\text{ = }\frac{opposite}{adjacent} \end{gathered}[/tex]
From the given ratios, we have:
opposite = a
adjacent = 4
hypothenuse = b
Hence, the value of sin x :
[tex]sin\text{ x = }\frac{a}{b}[/tex]
Answer:
[tex]sin\text{ x = }\frac{a}{b}\text{ \lparen Option C\rparen}[/tex]
