A tower stands vertically on the ground. From a point on the ground, which is `15 m`away from the foot of the tower, the angle of elevation of the top of the tower is found to be `60^@`. Find the height of the tower.

Options

A. `12sqrt3`
B. `15sqrt3`
C. `13sqrt3`
D. None

Explanation

To find the height of the tower using the given information, we can follow these steps:

### Step 1: Understand the problem
We have a tower standing vertically, and we are given the distance from a point on the ground to the foot of the tower, which is 15 meters. The angle of elevation from this point to the top of the tower is 60 degrees. We need to find the height of the tower.

### Step 2: Set up the right triangle
We can visualize the situation as a right triangle where:
- The height of the tower is the opposite side (let's denote it as \( H \)).
- The distance from the point on the ground to the foot of the tower is the adjacent side (which is 15 m).
- The angle of elevation is 60 degrees.

### Step 3: Use the tangent function
In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. Therefore, we can write:
\[ \tan(60^\circ) = \frac{H}{15} \]

### Step 4: Find the value of \( \tan(60^\circ) \)
From trigonometric tables or knowledge, we know:
\[ \tan(60^\circ) = \sqrt{3} \]

### Step 5: Substitute and solve for \( H \)
Now, substituting the value of \( \tan(60^\circ) \) into the equation:
\[ \sqrt{3} = \frac{H}{15} \]

To find \( H \), we can rearrange the equation:
\[ H = 15 \cdot \sqrt{3} \]

### Step 6: Calculate the height
Now, we can calculate the height:
\[ H = 15 \sqrt{3} \text{ meters} \]

### Conclusion
Thus, the height of the tower is \( 15\sqrt{3} \) meters.

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