A person is 5 feet tall and casts a shadow of 3 feet long. A nearby building casts a shadow of 15 feet 4 inches. What is the height of the building ?
To solve this problem, we can set up a proportion:
(person's height) / (person's shadow length) = (building's height) / (building's shadow length)
Let's convert the height and shadow length of the building to feet:
15 feet 4 inches = 15 + 4/12 = 15.33 feet
Using the given values, we can set up the proportion and solve for the building's height:
5 / 3 = (building's height) / 15.33
Cross-multiplying the proportion:
(5)(15.33) = (building's height)(3)
76.65 = (building's height)(3)
Dividing both sides by 3 to solve for the building's height:
building's height = 76.65 / 3 = 25.55 feet
Therefore, the height of the building is approximately 25.55 feet.