In the diagram, A represents the base of the building, B represents the top of the building, and PQ is the distance between points P and Q.
We have two right triangles, one at point P and another at point Q. The opposite side of each triangle represents the height of the building (h), and the adjacent side represents the distance from each observation point to the base of the building.
Using trigonometry, we can set up the following equations:
For triangle APB:
tan(42°) = h / x
For triangle BQA:
tan(33°) = h / (94 - x)
Here, x represents the distance from point P to the base of the building.
Solving the first equation for x:
x = h / tan(42°)
Substituting this value of x into the second equation:
tan(33°) = h / (94 - (h / tan(42°)))
Now, we can solve this equation to find the value of h.
By substituting the values into the equation and solving for h, we find:
h ≈ 52.1 meters
Therefore, the height of the building, to the nearest tenth of a meter, is approximately 52.1 meters.