Question

what is the value of sin(a)?

Explanation:

Step1: Recall sine - definition

$\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Identify sides in right - triangle

In right - triangle $ABC$, for $\angle A$, the opposite side to $\angle A$ is $BC$ and hypotenuse is $AB$. Triangles are similar, and in $\triangle XYZ$, we can use ratios. Since $\sin(A)=\sin(X)$ and in $\triangle XYZ$, $\sin(X)=\frac{YZ}{XY}$.

Step3: Calculate sine value

$\sin(A)=\frac{6}{10} = 0.6$

Answer:

$0.6$