A tree casts a shadow that is 70 feet long. At the same time a person is standing nearby who is 5 feet 6 inches tall and their shadpw os 60 inches long. What is the proportion and what is the height of the tree?
77 feet
To find the proportion between the person's height and the length of their shadow, we need to convert the person's height and shadow length to the same unit of measurement. Let's convert the person's height to feet:
Height of person = 5 feet + 6 inches
= 5 + (6/12) feet
= 5.5 feet
Now, let's convert the person's shadow length to feet:
Shadow length of person = 60 inches
= 60/12 feet
= 5 feet
The proportion between the person's height and their shadow can be written as:
(person's height)/(person's shadow) = (tree's height)/(tree's shadow)
Substituting the values we found:
5.5 feet / 5 feet = (tree's height) / 70 feet
Now, let's solve for the tree's height:
(tree's height) = (5.5 feet / 5 feet) * 70 feet
= (5.5/5) * 70 feet
= 77 feet
Therefore, the height of the tree is 77 feet.