Question

The thickness of a dipping coal bed measured along a vertical drill hole is 15 m. If the dip of the coal bed is 30⁰, the orthogonal thickness of the coal bed is ___________ m. (Round off to the nearest integer)

Answer 1

Correct Answer: 13

Calculating the Orthogonal Thickness of a Coal Bed 

Step 1: Understanding the Formula

The orthogonal thickness (t) of the coal bed is related to the thickness (T) measured along the drill hole and the dip angle (θ) by the following formula:

\[ t = T \times \cos(\theta) \]

Where:

• T is the thickness measured along the drill hole (15 m).
• \(\theta\) is the dip angle (30°).

Step 2: Substituting the Given Values

Substituting the given values into the formula:

\[ t = 15 \, \text{m} \times \cos(30^\circ) \approx 15 \, \text{m} \times 0.866 \approx 13 \, \text{m} \]

Final Answer:

The orthogonal thickness of the coal bed is: 13 m (rounded to the nearest integer).