A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be `45^@`. Find the height of the tower.

Answer

To find the height of the tower, we can use the concept of trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (height of the tower) and the adjacent side (distance from the tower).

### Step-by-Step Solution:

1. **Identify the Components**:
- Let the height of the tower be \( h \) meters.
- The distance from the point on the ground to the foot of the tower is \( 30 \) meters.
- The angle of elevation to the top of the tower is \( 45^\circ \).

2. **Use the Tangent Function**:
The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. Therefore, we can write:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]
For our problem:
\[ \tan(45^\circ) = \frac{h}{30} \]

3. **Calculate \( \tan(45^\circ) \)**:
We know that:
\[ \tan(45^\circ) = 1 \]
Thus, substituting this value into the equation gives:
\[ 1 = \frac{h}{30} \]

4. **Solve for \( h \)**:
To find \( h \), we can rearrange the equation:
\[ h = 1 \times 30 \]
Therefore:
\[ h = 30 \text{ meters} \]

5. **Conclusion**:
The height of the tower is \( 30 \) meters.