\text{A man, 1.8 m tall, is standing on a 1.0 m high platform near its edge, to observe the top of a building. The building is at a distance of 25√3 m away from the platform. The angle of elevation from his eye to the top of the building is 30°. The height (in m) of the building is:}

The correct option is 27.8.

Let us break down the problem step-by-step to calculate the height of the building.

Step 1: Understand the positions and heights of the observer and the platform
The man is standing on a platform.
Height of the platform = 1.0 m
Height of the man = 1.8 m
Therefore, the height of the man's eye above the ground level is:
Height of eye level = Height of platform + Height of man
Height of eye level = 1.0 m + 1.8 m = 2.8 m

Step 2: Set up the trigonometry for the building
Let the total height of the building be $H$ meters.
The distance from the platform (where the man is standing) to the building is given as:
$d=25\sqrt{3}\text{m}$
The angle of elevation from the man's eye to the top of the building is 30°.
Let $h$ be the height of the building above the man's eye level.

Using the tangent trigonometric ratio for the right-angled triangle formed by the eye level, the horizontal distance, and the top of the building:
$\tan (30°)=\frac{h}{d}$
We know that $\tan (30°)=\frac{1}{\sqrt{3}}$. Substituting this value:
$\frac{1}{\sqrt{3}}=\frac{h}{25\sqrt{3}}$
Solving for $h$:
$h=\frac{25\sqrt{3}}{\sqrt{3}}=25\text{m}$

Step 3: Calculate the total height of the building
The total height of the building $H$ is the sum of the height of the man's eye level above the ground and the height $h$ of the building above his eye level:
Total Height $H=\text{Height of eye level}+h$
$H=2.8\text{m}+25\text{m}=27.8\text{m}$

Thus, the height of the building is 27.8 m, which matches the option 27.8.