`Delta ABC` has a right angle at A. If `BC = sqrt2 and AB = AC = 1` then `sin B ` is equal to
(a) `(1)/(sqrt2)`
(b) `sqrt2`
(c) `(sqrt3)/(2)`
(d) `sqrt3`

Options

A. `(1)/(sqrt2)`
B. `sqrt2`
C. `(sqrt3)/(2)`
D. `sqrt3`

Answer

To solve the problem, we need to find the value of \( \sin B \) in triangle \( ABC \) where \( A \) is the right angle. Given that \( BC = \sqrt{2} \) and \( AB = AC = 1 \), we can follow these steps:

### Step 1: Identify the triangle and sides
In triangle \( ABC \):
- \( A \) is the right angle.
- \( AB = 1 \) (one leg of the triangle).
- \( AC = 1 \) (the other leg of the triangle).
- \( BC = \sqrt{2} \) (the hypotenuse).

### Step 2: Use the definition of sine
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For angle \( B \):
\[ \sin B = \frac{\text{opposite side to } B}{\text{hypotenuse}} \]

### Step 3: Identify the opposite side and hypotenuse
In triangle \( ABC \):
- The side opposite to angle \( B \) is \( AC \), which has a length of \( 1 \).
- The hypotenuse is \( BC \), which has a length of \( \sqrt{2} \).

### Step 4: Substitute the values into the sine formula
Now we can substitute the values into the sine formula:
\[ \sin B = \frac{AC}{BC} = \frac{1}{\sqrt{2}} \]

### Step 5: Simplify the expression
The expression \( \frac{1}{\sqrt{2}} \) can also be rationalized, but it is not necessary for this problem. The value is already in a suitable form.

### Conclusion
Thus, the value of \( \sin B \) is:
\[ \sin B = \frac{1}{\sqrt{2}} \]
This corresponds to option (a).