On one sunny afternoon, the movie theater casts a shadow of 30 feet. At the same time of day, A tree is casting a shadow of 10 feet. What is the height of the movie theater?
How tall is the tree?
To find the height of the movie theater, we can use proportions. The ratio of the height of the movie theater to the length of its shadow is equal to the ratio of the height of the tree to the length of its shadow.
Let's assign variables to the unknowns:
- Height of the movie theater: h
- Length of the movie theater's shadow: x
- Height of the tree: t
- Length of the tree's shadow: y
According to the given information:
x = 30 feet (length of the movie theater's shadow)
y = 10 feet (length of the tree's shadow)
The proportion can be set up as:
h/x = t/y
Substituting the known values:
h/30 = t/10
To find the height of the movie theater (h), we need to find the value of t (height of the tree) first.
To find the value of t, we can cross multiply and solve for t:
10h = 30t
Now, we can solve for t:
t = (10h)/30
t = h/3
Since the height of the tree (t) is equal to the height of the movie theater (h) divided by 3, the height of the theater is three times the height of the tree.
Therefore, the height of the movie theater is three times the height of the tree. By knowing the height of the tree, we can find the height of the movie theater.