Question

The length of an objects shadow varies directly with its height. A boy who is 4 feet 6 inches tall casts a shadow that is 6 feet 3 inches long. What is the height of a tree that casts a shadow that is 25 feet long?

Answer 1

Problem:

The length of an objects shadow varies directly with its height. A boy who is 4 feet 6 inches tall casts a shadow that is 6 feet 3 inches long. What is the height of a tree that casts a shadow that is 25 feet long?

Solution:

According to the figures above:

$$t g \alpha = \frac {4 f e e t 6 i n c h e s}{6 f e e t 3 i n c h e s} = \frac {4 . 5 f e e t}{6 . 2 5 f e e t} = \frac {h}{2 5 f e e t}$$

Thus

$$h = \frac {2 5 * 4 . 5}{6 . 2 5} = 1 8 f e e t$$

Answer: height of a tree is $h = 18$ feet.