Final answer:
To find the height of the building, set up a proportion using the height and shadow length of a man and then apply this ratio to the building and its shadow. By solving the proportion, the building is approximately 25.5 ft tall.
Step-by-step explanation:
The student is asking for help with a problem involving similar triangles and proportionality. In this case, we can find the height of the building by using the ratio of the height of a man to his shadow, and applying this same ratio to the building and its shadow. Here's how we solve it:
- First, we have a 6 ft tall man casting a 3.5 ft shadow.
- Next, we set up the proportion 6 ft / 3.5 ft = x ft / 14.875 ft, where x represents the height of the building.
- To solve for x, we cross-multiply: 6 ft × 14.875 ft = 3.5 ft × x ft.
- Then, we divide both sides of the equation by 3.5 ft to find the height of the building, which gives us x = (6 ft × 14.875 ft) / 3.5 ft.
- Solving for x, we find that the building is approximately 25.5 ft tall.