If ` sqrt(3) sin theta = cos theta and theta" is an acute angle, find the value of " theta.`

Explanation

To solve the equation \( \sqrt{3} \sin \theta = \cos \theta \) for the acute angle \( \theta \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ \sqrt{3} \sin \theta = \cos \theta \]

### Step 2: Divide both sides by \( \cos \theta \)
To isolate \( \tan \theta \), we can divide both sides of the equation by \( \cos \theta \) (assuming \( \cos \theta \neq 0 \)):
\[ \frac{\sqrt{3} \sin \theta}{\cos \theta} = 1 \]
This simplifies to:
\[ \sqrt{3} \tan \theta = 1 \]

### Step 3: Solve for \( \tan \theta \)
Now, we can solve for \( \tan \theta \):
\[ \tan \theta = \frac{1}{\sqrt{3}} \]

### Step 4: Find the angle \( \theta \)
We know that \( \tan \theta = \frac{1}{\sqrt{3}} \) corresponds to a specific angle. The angle whose tangent is \( \frac{1}{\sqrt{3}} \) is:
\[ \theta = 30^\circ \]

### Step 5: Verify that \( \theta \) is acute
Since \( 30^\circ \) is indeed an acute angle, we have our solution.

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

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