If `a=1`, `b=sqrt3` and `angleA`=`30^(@)`, find the value of the `angle B`:

Options

A. `60^(@)`
B. `30^(@)`
C. `120^(@)`
D. either (a) or (c )

Answer

To find the value of angle B in triangle ABC, given that \( a = 1 \), \( b = \sqrt{3} \), and \( \angle A = 30^\circ \), we can use the Law of Sines, which states:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

### Step 1: Write down the known values.
We know:
- \( a = 1 \)
- \( b = \sqrt{3} \)
- \( \angle A = 30^\circ \)

### Step 2: Use the Law of Sines.
According to the Law of Sines:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} \]

Substituting the known values:

\[ \frac{1}{\sin 30^\circ} = \frac{\sqrt{3}}{\sin B} \]

### Step 3: Calculate \( \sin 30^\circ \).
We know that:

\[ \sin 30^\circ = \frac{1}{2} \]

### Step 4: Substitute \( \sin 30^\circ \) into the equation.
Now substitute \( \sin 30^\circ \) into the equation:

\[ \frac{1}{\frac{1}{2}} = \frac{\sqrt{3}}{\sin B} \]

This simplifies to:

\[ 2 = \frac{\sqrt{3}}{\sin B} \]

### Step 5: Rearrange to find \( \sin B \).
Now, rearranging gives:

\[ \sin B = \frac{\sqrt{3}}{2} \]

### Step 6: Determine the angle B.
We know that:

\[ \sin B = \frac{\sqrt{3}}{2} \]

This corresponds to:

\[ B = 60^\circ \]

### Conclusion:
Thus, the value of angle B is:

\[ \angle B = 60^\circ \]

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