First, we need to find the height of the window and the height of the building by using the tangent function with the given angles of elevation.
tan(28°) = (window height - 5 ft) / 75 ft
window height = 75 ft * tan(28°) + 5 ft ≈ 47.87 ft
tan(42°) = (building height - 5 ft) / 75 ft
building height = 75 ft * tan(42°) + 5 ft ≈ 69.44 ft
Now we can find the height difference between the rooftop and the windowsill:
roof_to_windowsill_height = building height - window height ≈ 69.44 ft - 47.87 ft ≈ 21.57 ft
Now we can use the Pythagorean theorem to find the windowsill-to-roof distance:
distance² = 75 ft² + (roof_to_windowsill_height)²
distance² = 75² + 21.57² ≈ 6364.64
distance ≈ sqrt(6364.64) ≈ 79.78 ft
Now, we have to subtract the distance from the firefighter to the building (75 ft) to find the distance between the windowsill and the rooftop:
windowsill_to_roof_distance = 79.78 ft - 75 ft ≈ 4.78 ft
The nearest answer is:
a. about 28 ft.