In fig height of a building is `h+2` and point C is h m from the foot of the building. Find the angle of elevation of the top of the building from a point 2 m from point C.

Answer

To solve the problem step by step, we will analyze the given information and apply trigonometric principles.

### Step 1: Understand the problem
We have a building with a height of \( h + 2 \) meters. Point C is located \( h \) meters from the foot of the building, and we need to find the angle of elevation (let's call it \( \theta \)) from point D, which is 2 meters away from point C.

### Step 2: Identify the distances
- The height of the building (AB) = \( h + 2 \) meters.
- Distance from the foot of the building to point C (BC) = \( h \) meters.
- Distance from point C to point D (CD) = 2 meters.
- Therefore, the total distance from the foot of the building to point D (BD) = BC + CD = \( h + 2 \) meters.

### Step 3: Set up the tangent function
Using the definition of the tangent function in a right triangle:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]
Here, the opposite side is the height of the building (AB = \( h + 2 \)) and the adjacent side is the distance from the foot of the building to point D (BD = \( h + 2 \)).

### Step 4: Write the equation
Substituting the values into the tangent function:
\[ \tan(\theta) = \frac{h + 2}{h + 2} \]
This simplifies to:
\[ \tan(\theta) = 1 \]

### Step 5: Find the angle
We know that \( \tan(45^\circ) = 1 \), therefore:
\[ \theta = 45^\circ \]

### Conclusion
The angle of elevation of the top of the building from point D is \( 45^\circ \).