At a point 15 m away from the base of a 15 m high house, the angle of elevation of the top is

Options

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

Answer

To solve the problem step by step, we will use the concept of height and distance along with trigonometric ratios.

### Step 1: Understand the problem
We have a house that is 15 meters high, and we are standing 15 meters away from the base of the house. We need to find the angle of elevation from our point to the top of the house.

### Step 2: Draw a diagram
Let's visualize the situation:
- Let point A be the top of the house.
- Let point B be the base of the house.
- Let point C be the point where we are standing.
- The height of the house (AB) = 15 m.
- The distance from the point (C) to the base of the house (B) = 15 m.

### Step 3: Identify the right triangle
In triangle ABC:
- AB = height of the house = 15 m (opposite side)
- BC = distance from the point to the base of the house = 15 m (adjacent side)

### Step 4: Use the tangent function
We will use the tangent of the angle of elevation (θ):
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{AB}{BC} \]
Substituting the values:
\[ \tan(θ) = \frac{15}{15} = 1 \]

### Step 5: Find the angle
Now, we need to find the angle whose tangent is 1. We know that:
\[ \tan(45°) = 1 \]
Thus, we can conclude that:
\[ θ = 45° \]

### Step 6: Conclusion
The angle of elevation of the top of the house from the point 15 m away is 45°.

### Final Answer
The angle of elevation is **45 degrees**.

---