A person standing at point P sees angle of elevation of the top of a building, whose base is 50 meters away, to be `60^(@)`. Another building whose base is 20 meters away from the base of the first building and is between the observer and first building has height h meters, then the maximum possible height (in meters) of this second building is `("Take "sqrt3=1.73)`

Answer

To solve the problem step by step, we will use trigonometric principles and the given information about the buildings and angles.

### Step 1: Understand the Setup
We have two buildings:
- Building A (the first building) is at a distance of 50 meters from point P.
- Building B (the second building) is 20 meters away from Building A, which means it is 30 meters away from point P (50 - 20 = 30 meters).

### Step 2: Determine the Height of Building A
The angle of elevation to the top of Building A from point P is given as \(60^\circ\). We can use the tangent function to find the height of Building A.

Let \(h_A\) be the height of Building A. According to the tangent function:
\[ \tan(60^\circ) = \frac{h_A}{50} \]
We know that \(\tan(60^\circ) = \sqrt{3}\). Therefore, we can write:
\[ \sqrt{3} = \frac{h_A}{50} \]
From this, we can solve for \(h_A\):
\[ h_A = 50\sqrt{3} \]

### Step 3: Calculate the Height of Building A
Now substituting the value of \(\sqrt{3} \approx 1.73\):
\[ h_A = 50 \times 1.73 = 86.5 \text{ meters} \]

### Step 4: Determine the Maximum Height of Building B
Now we need to find the maximum possible height \(h_B\) of Building B, which is at a distance of 30 meters from point P. The angle of elevation to the top of Building B can also be calculated using the tangent function:
\[ \tan(60^\circ) = \frac{h_B}{30} \]
Again, substituting \(\tan(60^\circ) = \sqrt{3}\):
\[ \sqrt{3} = \frac{h_B}{30} \]
Solving for \(h_B\):
\[ h_B = 30\sqrt{3} \]

### Step 5: Calculate the Height of Building B
Substituting the value of \(\sqrt{3} \approx 1.73\):
\[ h_B = 30 \times 1.73 = 51.9 \text{ meters} \]

### Conclusion
The maximum possible height of the second building (Building B) is \(51.9\) meters.