Anand is watching a circus artist climbing a 20m long rope which is tightly stretched and tied from the top of vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is `30^(@)`.

Answer

To find the height of the pole using the information given in the problem, we can follow these steps:

### Step 1: Understand the Problem
We have a vertical pole and a rope that is tied from the top of the pole to the ground, forming a right triangle. The length of the rope is given as 20 meters, and the angle between the rope and the ground is 30 degrees.

### Step 2: Identify the Triangle
In this right triangle:
- The height of the pole (which we need to find) is the perpendicular side (let's call it \( h \)).
- The length of the rope is the hypotenuse, which is 20 meters.
- The angle made with the ground is 30 degrees.

### Step 3: Use the Sine Function
We can use the sine function, which relates the angle to the opposite side (height of the pole) and the hypotenuse. The formula is:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
In our case:
\[ \sin(30^\circ) = \frac{h}{20} \]

### Step 4: Substitute the Value of Sine
We know that:
\[ \sin(30^\circ) = \frac{1}{2} \]
Substituting this into the equation gives:
\[ \frac{1}{2} = \frac{h}{20} \]

### Step 5: Solve for \( h \)
To find \( h \), we can rearrange the equation:
\[ h = 20 \times \frac{1}{2} \]
\[ h = 10 \text{ meters} \]

### Conclusion
The height of the pole is 10 meters.