Question

in the triangle, $\frac{a}{c}$ represents which ratio? cos c sin b sin c tan b

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
For angle $C$, the opposite side is $AB = 4$, the adjacent side is $AC = 3$, and the hypotenuse is $BC = 5$. So, $\cos C=\frac{AC}{BC}=\frac{3}{5}$, $\sin C=\frac{AB}{BC}=\frac{4}{5}$.
For angle $B$, the opposite side is $AC = 3$, the adjacent side is $AB = 4$, and the hypotenuse is $BC = 5$. So, $\sin B=\frac{AC}{BC}=\frac{3}{5}$, $\tan B=\frac{AC}{AB}=\frac{3}{4}$.

Step2: Identify the ratio $\frac{3}{5}$

We see that $\sin B=\frac{AC}{BC}=\frac{3}{5}$.

Answer:

$\sin B$