Question

A tree cast a 25 foot shadow. At the same time, a 6 foot pole cast a shadow 4.5 feet long. How tall is the tree

Answer 1

`33(1)/(3)` ft

Explanation:

Think about the ratio of shadow to actual height.

First, make a ratio table demonstrating the scale factor of the shadow to the height of the object:

height : shadow

6 ft : 4.5 ft

To get rid of the decimal, multiply by 10 on both sides:

60 ft : 45 ft

In order to get the shadow to 25 ft, multiply both sides by 25/45, which simplifies to 5/9:

height : shadow

6 ft : 4.5 ft

60 ft : 45 ft

*(5/9) : *(5/9)

33 1/3 ft : 25 ft

The answer is the height corresponding to the shadow length 25 ft in the table, in this case,
`33(1)/(3)`.