From a point A which is 60 metres from the base of a building B and on the same level, the angle of elevation to the top of the building C is 51°, and to the top of the flagpole D on top of the buildi

Let $AB$ be the distance from point A to the base of the building, so $AB = 60 \text{ m}$.
Let $BC$ be the height of the building.
Let $CD$ be the height of the flagpole.
Let $BD$ be the total height from the ground to the top of the flagpole, so $BD = BC + CD$.

From the given angles of elevation:
For the building: $\tan(51^\circ) = \frac{BC}{AB}$
For the building with flagpole: $\tan(56^\circ) = \frac{BD}{AB}$

$$BC = AB \times \tan(51^\circ)$$ $$BC = 60 \text{ m} \times \tan(51^\circ)$$ $$BC = 60 \text{ m} \times 1.23490$$ $$BC \approx 74.094 \text{ m}$$

$$BD = AB \times \tan(56^\circ)$$ $$BD = 60 \text{ m} \times \tan(56^\circ)$$ $$BD = 60 \text{ m} \times 1.48256$$ $$BD \approx 88.954 \text{ m}$$

The height of the flagpole is the total height minus the height of the building.

$$CD = BD - BC$$ $$CD = 88.954 \text{ m} - 74.094 \text{ m}$$ $$CD = \boxed{14.86 \text{ m}}$$