To determine the sine of angle $B$ in the triangle, we need to use the definition of sine for a right triangle, which is:

$\sin(B) = \frac{\text{opposite side to } B}{\text{hypotenuse}}$

From the image:

• The side opposite angle $B$ is $8$ (side $AC$).
• The adjacent side to angle $B$ is $6$ (side $AB$).
• The hypotenuse $BC$ can be found using the Pythagorean theorem:

$BC^2 = AB^2 + AC^2$ $BC^2 = 6^2 + 8^2 = 36 + 64 = 100$ $BC = \sqrt{100} = 10$

Thus, the hypotenuse $BC = 10$. Now, we can calculate $\sin(B)$:

$\sin(B) = \frac{AC}{BC} = \frac{8}{10} = \frac{4}{5}$

Therefore, the correct answer is:

$\boxed{4/5} \quad \text{(option c)}$

Would you like further details or have any other questions?

Here are five related questions for practice:

1. What is the cosine of angle $B$ in the given triangle?
2. What is the tangent of angle $B$?
3. If the triangle were scaled up, keeping the same angles, how would the sine of angle $B$ change?
4. Can you find the area of the triangle using the sine of angle $B$?
5. What is the sine of angle $A$?

Tip: Remember, sine is always the ratio of the opposite side to the hypotenuse, no matter the size of the triangle as long as the angles are fixed!