A telegraph post is bent at a point above the ground due to storm .Its top just meets the ground at a distance of `8sqrt(3)` metres from its foot and makes an angle of `30^(@)` , then the height of the post is :

Options

A. 16 metres
B. 23 metres
C. 24 metres
D. 10 metres

Answer

To solve the problem, we need to find the height of the telegraph post that is bent due to a storm. We will use trigonometric ratios to determine the height.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- The telegraph post is bent at a point above the ground.
- The top of the post touches the ground at a distance of \(8\sqrt{3}\) meters from its foot.
- The angle formed with the ground is \(30^\circ\).

2. **Visualizing the Situation**:
- We can visualize this scenario as a right triangle where:
- \(A\) is the point where the post is bent.
- \(B\) is the foot of the post.
- \(C\) is the point where the top of the post touches the ground.
- The distance \(BC\) (the horizontal distance from the foot of the post to the point where the top touches the ground) is \(8\sqrt{3}\) meters.

3. **Identifying the Triangle**:
- In triangle \(ABC\):
- \(AB\) is the vertical height of the post above point \(A\).
- \(AC\) is the length of the post from point \(A\) to point \(C\) (the hypotenuse).
- The angle \(CAB\) is \(30^\circ\).

4. **Using the Tangent Function**:
- We can use the tangent function to find \(AB\):
\[ \tan(30^\circ) = \frac{AB}{BC} \]
- We know that \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\) and \(BC = 8\sqrt{3}\):
\[ \frac{1}{\sqrt{3}} = \frac{AB}{8\sqrt{3}} \]
- Cross-multiplying gives:
\[ AB = 8 \]

5. **Using the Sine Function**:
- Now, we can use the sine function to find \(AC\):
\[ \sin(30^\circ) = \frac{AB}{AC} \]
- We know that \(\sin(30^\circ) = \frac{1}{2}\):
\[ \frac{1}{2} = \frac{8}{AC} \]
- Cross-multiplying gives:
\[ AC = 16 \]

6. **Calculating the Total Height of the Post**:
- The total height of the post is the sum of \(AB\) and \(AC\):
\[ \text{Height of the post} = AB + AC = 8 + 16 = 24 \text{ meters} \]

### Final Answer:
The height of the post is **24 meters**.