If `3tanA-5cosB=sqrt(3) and B=90^(@)`, find the value of A.

Answer

To solve the equation \(3\tan A - 5\cos B = \sqrt{3}\) given that \(B = 90^\circ\), we can follow these steps:

### Step 1: Substitute the value of \(B\)
Since \(B = 90^\circ\), we can substitute this value into the equation. We know that \(\cos 90^\circ = 0\).

\[ 3\tan A - 5\cos(90^\circ) = \sqrt{3} \]
This simplifies to:
\[ 3\tan A - 5 \cdot 0 = \sqrt{3} \]
So, we have:
\[ 3\tan A = \sqrt{3} \]

### Step 2: Isolate \(\tan A\)
Now, we can isolate \(\tan A\) by dividing both sides of the equation by 3:
\[ \tan A = \frac{\sqrt{3}}{3} \]

### Step 3: Simplify \(\tan A\)
We can recognize that \(\frac{\sqrt{3}}{3}\) can be rewritten using the identity:
\[ \tan A = \frac{1}{\sqrt{3}} \]

### Step 4: Find the angle \(A\)
We know that \(\tan 30^\circ = \frac{1}{\sqrt{3}}\). Therefore, we can conclude:
\[ A = 30^\circ \]

### Final Answer
Thus, the value of \(A\) is:
\[ \boxed{30^\circ} \]

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