Question

A man wants to attach a string to the top of a building and to a point on the ground near the end of the building's shadow at 4:00 pm. He is 6 feet tall and his shadow is 8 feet long at 4:00. The building is 42 feet tall. About how long will the string have to be?

Answer 1

65.33 ft

Explanation:

To determine the length of the string needed, we can use similar triangles and the concept of proportional relationships. We can consider the man, the building, and their respective shadows as forming similar triangles. The ratio of the man's height to his shadow length is the same as the ratio of the building's height to its shadow length. The man's height is 6 feet, and his shadow is 8 feet long. The building's height is 42 feet. Using the proportionality between the man and the building: 6 feet / 8 feet = 42 feet / x To solve for x, the length of the string, we can cross-multiply and then divide: 6 feet * x = 8 feet * 42 feet x = (8 feet * 42 feet) / 6 feet x = 56 feet * 7 feet / 6 feet x = 392 feet / 6 feet x ≈ 65.33 feet Therefore, the string will need to be approximately 65.33 feet long.