If `A+B=90^(@)andtanA=sqrt(3)`, then find the value of B.

Answer

To solve the problem, we need to find the value of \( B \) given that \( A + B = 90^\circ \) and \( \tan A = \sqrt{3} \).

### Step-by-step Solution:

1. **Understanding the relationship between A and B**:
We know that:
\[ A + B = 90^\circ \]
This implies that \( B = 90^\circ - A \).

2. **Using the value of \( \tan A \)**:
We are given that:
\[ \tan A = \sqrt{3} \]
We know from trigonometric values that:
\[ \tan 60^\circ = \sqrt{3} \]
Therefore, we can conclude that:
\[ A = 60^\circ \]

3. **Substituting the value of A into the equation for B**:
Now that we have \( A \), we can substitute it back into the equation for \( B \):
\[ B = 90^\circ - A = 90^\circ - 60^\circ \]

4. **Calculating the value of B**:
\[ B = 30^\circ \]

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

### Final Answer:
\[ B = 30^\circ \]