In this problem, there are two right triangles formed. One is formed with the height of the building as its vertical side, and the other is formed with the height of the windowsill as its vertical side. We can use the tangent function to solve both triangles from the angle of elevation information.
Let's call the height of the building, H and the height to the windowsill, W.
For the building height,
tan(42°) = H / 75
H = 75 * tan(42°)
For the windowsill height,
tan(28°) = W / 75
W = 75 * tan(28°)
Now, we want to find the difference between these two heights (ΔH) and also account for the firefighter's eye level which is 5 ft. above the ground.
ΔH = H - W
ΔH = (75 * tan(42°)) - (75 * tan(28°))
Calculating the values and subtracting,
ΔH = (75 * 0.9004) - (75 * 0.5317)
ΔH = 67.53 - 39.8775
ΔH = 27.6525
However, we need to include the height from the ground to firefighter's eyes, so we add that 5 ft. to the difference in heights:
ΔH = 27.6525 + 5
ΔH = 32.6525
Hence, the height of the windowsill above the firefighter's eyes is about 33 ft. The correct answer is choice b.