Final answer:
Using trigonometry with a given angle and ladder length, the height of the house is calculated to be approximately 16.7 feet when rounded to the nearest tenth of a foot, corresponding to option A, 16.6 ft.
Step-by-step explanation:
The question is asking to determine the height of the house when a ladder is placed against it at a known angle. Given a 25-foot ladder forms an angle of 41.5° with the wall, we can use trigonometry to find the height of the house. Specifically, the sine function relates the opposite side (the height of the house we want to find) to the hypotenuse (the length of the ladder).
To solve for the height (h) of the house:
- sin(41.5°) = h / 25 feet
- h = 25 feet * sin(41.5°)
- h ≈ 25 feet * 0.6669
- h ≈ 16.6725 feet
Rounded to the nearest tenth of a foot, the height of the house is approximately 16.7 feet. Therefore, the closest answer to the nearest tenth of a foot is option A, 16.6 ft.