If `A-B=30^(@)andsinA=(sqrt(3))/(2)`,then find the value of B.

Answer

To solve the problem step by step, we follow these instructions:

### Step 1: Understand the given equations
We have two equations:
1. \( A - B = 30^\circ \)
2. \( \sin A = \frac{\sqrt{3}}{2} \)

### Step 2: Identify the angle A
We know that \( \sin 60^\circ = \frac{\sqrt{3}}{2} \). Therefore, we can equate:
\[ \sin A = \sin 60^\circ \]
This implies that:
\[ A = 60^\circ \]
(because sine is positive in the first quadrant and we are looking for angles in the range of 0° to 90°).

### Step 3: Substitute the value of A into the first equation
Now, we substitute \( A = 60^\circ \) into the first equation:
\[ 60^\circ - B = 30^\circ \]

### Step 4: Solve for B
To find \( B \), we rearrange the equation:
\[ B = 60^\circ - 30^\circ \]
\[ B = 30^\circ \]

### Final Answer
Thus, the value of \( B \) is \( 30^\circ \).

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