If `Delta`ABC is right - angle at B, AB = 6 units `angle = 30^@` then AC is equal to

Options

A. 12 units
B. 15 units
C. 8 units
D. 10 units

Answer

To find the length of AC in triangle ABC, where angle B is a right angle, AB = 6 units, and angle C = 30 degrees, we can use the sine function.

### Step-by-Step Solution:

1. **Identify the triangle and known values**:
- Triangle ABC is a right triangle with angle B = 90 degrees.
- AB (the side opposite angle C) = 6 units.
- Angle C = 30 degrees.

2. **Use the sine function**:
- In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
- Therefore, we can write:
\[ \sin C = \frac{AB}{AC} \]
- Substituting the known values:
\[ \sin 30^\circ = \frac{6}{AC} \]

3. **Calculate \(\sin 30^\circ\)**:
- We know that \(\sin 30^\circ = \frac{1}{2}\).

4. **Set up the equation**:
- Now substituting \(\sin 30^\circ\) into the equation:
\[ \frac{1}{2} = \frac{6}{AC} \]

5. **Cross-multiply to solve for AC**:
- Cross-multiplying gives:
\[ 1 \cdot AC = 2 \cdot 6 \]
- Therefore:
\[ AC = 12 \]

6. **Conclusion**:
- The length of AC is 12 units.

### Final Answer:
AC = 12 units.