Question

The shadow cast by an object on a sunny day is directly proportional to the height of the object. If a person 82 inches tall casts a shadow 57 inches long, how tall is a tree which casts

shadow 31 feet in length? Round to the nearest hundredth if necessary
A. 150.77 feet
B. 44.6 feet
C. 69.5 feet
D. 21.55 feet

Answer 1

Given :-

• Height of person = 82 inches
• Shadow of person = 57 inches
• Shadow of another person = 31 ft

To Find :-

Height of person

Solution :-

We may notice that they are in proportion

So,

Let the length be x

82/57 = x/31

57 × x = 82 × 31

57x = 2542

x = 2542/57

x = 44.6 ft

`\\`

Answer 2

B. 44.6 feet

Explanation:

To find the height of the tree, create a proportion where x is its height:

`(82)/(57)` =
`(x)/(31)`

Cross multiply and solve for x:

57x = 2542

x = 44.6

So, the tree is B, 44.6 feet