If a flagstaff of 6 m high placed on the top of a tower throws a shadow of `2 sqrt(3)` meters along the ground. Let `theta` be the angle (in degrees) that the sun makes with the ground, then the value of `sqrt(3) tan theta` = _____________ .

Answer

To solve the problem step by step, we will analyze the situation involving the flagstaff, the tower, and the shadows created by the sun.

### Step 1: Understand the Problem
We have a flagstaff of height 6 m placed on top of a tower. The shadow of the flagstaff on the ground is given as \(2\sqrt{3}\) m. We need to find the value of \(\sqrt{3} \tan \theta\), where \(\theta\) is the angle that the sun makes with the ground.

### Step 2: Draw a Diagram
Draw a right triangle where:
- The height of the flagstaff (6 m) is the vertical side (perpendicular).
- The length of the shadow (\(2\sqrt{3}\) m) is the horizontal side (base).
- The angle \(\theta\) is formed between the ground and the line from the top of the flagstaff to the tip of the shadow.

### Step 3: Set Up the Trigonometric Ratio
Using the definition of tangent in a right triangle:
\[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{6}{2\sqrt{3}} \]

### Step 4: Simplify the Expression
Now, simplify \(\tan \theta\):
\[ \tan \theta = \frac{6}{2\sqrt{3}} = \frac{3}{\sqrt{3}} \]

### Step 5: Calculate \(\sqrt{3} \tan \theta\)
Now, we need to find \(\sqrt{3} \tan \theta\):
\[ \sqrt{3} \tan \theta = \sqrt{3} \cdot \frac{3}{\sqrt{3}} = 3 \]

### Final Answer
Thus, the value of \(\sqrt{3} \tan \theta\) is:
\[ \boxed{3} \]