Question

in the triangle, $\frac{4}{5}$ represents which ratio?
a
4
b
3
5
c
sin c
sin b
cos c
tan b

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Analyze for angle C

For $\angle C$, the opposite side is $AB = 4$, the adjacent side is $AC = 3$, and the hypotenuse is $BC = 5$. So, $\sin C=\frac{AB}{BC}=\frac{4}{5}$, $\cos C=\frac{AC}{BC}=\frac{3}{5}$, $\tan C=\frac{AB}{AC}=\frac{4}{3}$.

Step3: Analyze for angle B

For $\angle B$, the opposite side is $AC = 3$, the adjacent side is $AB = 4$, and the hypotenuse is $BC = 5$. So, $\sin B=\frac{AC}{BC}=\frac{3}{5}$, $\cos B=\frac{AB}{BC}=\frac{4}{5}$, $\tan B=\frac{AC}{AB}=\frac{3}{4}$.

Answer:

$\sin C$