Answer: Let's draw a diagram to visualize the problem:
C D
| |
|h |
| |
|_ _ _ |_ _ _ _ _ _
A 10m B
In the diagram, A represents the top of the platform, B represents the bottom of the building, C represents the bottom of the building as seen from the top of the platform, D represents the top of the building as seen from the top of the platform, h represents the height of the building, and the angles of depression and elevation are labeled.
We can use trigonometry to solve for h. Let x be the distance from point A to point C, as shown in the diagram. Then we have:
tan(39°) = h/x (1)
tan(56°) = (h + 10)/x (2)
We can rearrange equation (1) to get:
x = h/tan(39°)
Substituting this into equation (2), we get:
tan(56°) = (h + 10)/(h/tan(39°))
Simplifying this expression, we get:
tan(56°) = (h + 10)tan(39°)/h
Multiplying both sides by h, we get:
h tan(56°) = (h + 10)tan(39°)
Expanding the right side, we get:
h tan(56°) = h tan(39°) + 10 tan(39°)
Subtracting h tan(39°) from both sides, we get:
h (tan(56°) - tan(39°)) = 10 tan(39°)
Dividing both sides by (tan(56°) - tan(39°)), we get:
h = 10 tan(39°) / (tan(56°) - tan(39°))
Using a calculator to evaluate this expression, we get:
h ≈ 17.5 meters
Therefore, the height of the building is approximately 18 meters to the nearest whole number.