To determine the sine ratio for angle \( g^\circ \) in triangle ACB where angle C is a right angle, we can use the definition of the sine function in a right triangle.
In triangle ACB:
- \( AC = x = 10 \) (adjacent to angle B)
- \( CB = y = 5 \) (opposite to angle B)
- \( AB = z = 11 \) (hypotenuse)
The sine of angle \( g \) (or \( \sin(g) \)) is defined as the ratio of the length of the opposite side to the length of the hypotenuse:
\[ \sin(g) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{CB}{AB} = \frac{y}{z} \]
Plugging in the values:
\[ \sin(g) = \frac{5}{11} \]
So the sine ratio for \( g^\circ \) is \( \frac{5}{11} \), which corresponds to the option "five elevenths." Thus, the answer is:
five elevenths.
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