The angle of elevation of the top of a 15 meters high tower from a point 15 metres aways from its foot is:

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To solve the problem of finding the angle of elevation of the top of a 15-meter high tower from a point 15 meters away from its foot, we can follow these steps:

### Step 1: Understand the Problem
We have a tower that is 15 meters tall, and we are observing it from a point that is 15 meters away from the base of the tower. We need to find the angle of elevation (θ) from that point to the top of the tower.

### Step 2: Draw a Right Triangle
We can visualize this situation as a right triangle where:
- The height of the tower (15 meters) is the perpendicular side (opposite side).
- The distance from the point to the foot of the tower (15 meters) is the base (adjacent side).

### Step 3: Use the Tangent Function
In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Therefore, we can write:
\[ \tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\text{Height of the tower}}{\text{Distance from the tower}} = \frac{15}{15} \]

### Step 4: Calculate the Tangent
Now we can calculate:
\[ \tan(θ) = \frac{15}{15} = 1 \]

### Step 5: Find the Angle
To find the angle θ, we need to determine the angle whose tangent is 1. We know that:
\[ \tan(45^\circ) = 1 \]
Thus, we have:
\[ θ = 45^\circ \]

### Conclusion
The angle of elevation of the top of the tower from the point 15 meters away from its foot is:
\[ \boxed{45^\circ} \]

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