Question

match the trigonometry formula to its correct ratio. reduce the ratio if necessary

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $A$, the opposite side is $BC = 16$, the adjacent side is $AB=12$, and the hypotenuse is $AC = 20$.

Step2: Calculate $\sin A$

$\sin A=\frac{BC}{AC}=\frac{16}{20}=\frac{4}{5}$.

Step3: Calculate $\cos A$

$\cos A=\frac{AB}{AC}=\frac{12}{20}=\frac{3}{5}$.

Answer:

$\sin A=\frac{4}{5}$, $\cos A=\frac{3}{5}$