Question

etermining a trigonometric ratio what is the value of sin (a)?

Explanation:

Step1: Recall sine - ratio formula

The formula for $\sin(A)$ in a right - triangle is $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse

Assuming $\triangle ABC$ is similar to $\triangle XYZ$ (since no other information about $\triangle ABC$ is given and we can use the known right - triangle $\triangle XYZ$ for the ratio). In right - triangle $\triangle XYZ$, for an angle corresponding to $\angle A$, the side opposite to the angle is $YZ = 6$ and the hypotenuse is $XY=10$.

Step3: Calculate the sine value

$\sin(A)=\frac{6}{10}=\frac{3}{5}$

Answer:

$\frac{3}{5}$