A storey building is 20 m away from a mango tree. The angle of depression from the top of the building to the mango is 68 degrees. The mango is 4.5 m above the ground. Calculate the height of the buil

Let $x$ be the vertical distance from the top of the building to the level of the mango. The horizontal distance from the base of the building to the tree is $20 \text{ m}$. The angle of depression from the top of the building to the mango is $68^\circ$. In the right-angled triangle formed, the opposite side to the angle of depression is $x$, and the adjacent side is $20 \text{ m}$.
We use the tangent function:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ $$\tan(68^\circ) = \frac{x}{20 \text{ m}}$$ $$x = 20 \text{ m} \times \tan(68^\circ)$$ $$x \approx 20 \text{ m} \times 2.4751$$ $$x \approx 49.502 \text{ m}$$

The total height of the building ($H$) is the sum of the vertical distance $x$ and the height of the mango above the ground ($4.5 \text{ m}$).

$$H = x + 4.5 \text{ m}$$ $$H \approx 49.502 \text{ m} + 4.5 \text{ m}$$ $$H \approx 54.002 \text{ m}$$

$$H \approx 54 \text{ m}$$

Comparing this to the given options, the closest option is (B).

The final answer is $\text{B) } \textbf{54 m}$.