Understanding the Geometry

The problem involves a right-angled triangle formed by the candle, its shadow on the table, and the line from the table surface to the candle's flame tip. The candle represents the height (opposite side), the shadow represents the base (adjacent side), and the angle of elevation is given.

Information Provided

• Height of the candle: \( H = 21 \text{ cm} \)
• Angle of elevation: \( \theta = 60^\circ \)
• We need to find the length of the shadow on the table (distance from the candle base), denoted as \( B \).

Applying Trigonometric Concepts

In a right-angled triangle, the tangent function relates the angle of elevation to the opposite and adjacent sides:

Substituting the known values:

Step-by-Step Calculation

1. Plug in the values: $ \tan(60^\circ) = \frac{21 \text{ cm}}{B} $
2. Use the known value for \( \tan(60^\circ) \), which is \( \sqrt{3} \): $ \sqrt{3} = \frac{21 \text{ cm}}{B} $
3. Rearrange the equation to solve for \( B \): $ B = \frac{21 \text{ cm}}{\sqrt{3}} $
4. Simplify the expression by rationalizing the denominator: $ B = \frac{21 \text{ cm}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{21\sqrt{3}}{3} \text{ cm} $
5. Further simplify the result: $ B = 7\sqrt{3} \text{ cm} $

Conclusion

The calculated length of the shadow is \( 7\sqrt{3} \text{ cm} \). Comparing this numerical value to the given options, which are in meters, we find that the value \( 7\sqrt{3} \) matches Option D.